Recent publications also posted on arXiv

Contents

List by year

2026

• B. Le Floch and P.G. LeFloch, Scattering laws for interfaces in self-gravitating matter flows, in preparation.

 

2025

• P.G. LeFloch and F.C. Mena, A first-order formulation of f(R) gravity in spherical symmetry, Also available at ArXiv: https://arxiv.org/abs/2512.06908.
• P.G. LeFloch and Y. Ma, and W. Zhang, The global nonlinear stability of Minkowski spacetime with self-gravitating massive Dirac fields, Monograph, October 2025. Also available at ArXiv: https://arxiv.org/abs/2510.20626 and HAL: https://hal.science/hal-05342436.

 

2024

• P.G. LeFloch and M.-D. Thanh, The Riemann Problem in Continuum Physics, Applied Mathematical Sciences, Book Series Springer Verlag, 2024 (about 300 pages).
• B. Le Floch and P.G. LeFloch, Optimal shielding for Einstein gravity, Class. Quantum Grav. 41 13LT02. Also available as ArXiv:2402.17598. Journal (DOI)
• P.G. LeFloch, F. Mena, and T.-C. Nguyen, Spherically symmetric evolution of self-gravitating massive fields, J. Differential Equ. 394 (2024) 31–97. Journal (DOI)
• P.G. LeFloch and Y. Ma, Nonlinear stability of self-gravitating massive fields, Annals of PDE 10 (2024), 16. Also available at ArXiv: https://arxiv.org/abs/1712.10045.
• P.G. LeFloch and Y. Ma, The Euclidean-hyperboloidal foliation method. Application to f(R) modified gravity, General Relativity and Gravitation 56 (2024), 66. Also available at ArXiv: https://arxiv.org/abs/2312.17712.
• S. Dong, P.G. LeFloch, and Z. Lei, The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded, Fundamental Research 4 (2024), 270–283. Also available at ArXiv: https://arxiv.org/abs/2103.07867. Journal (DOI)
• P.G. LeFloch, Reproducing Kernel Methods for Machine Learning, PDEs, and Statistics,, J.-M. Mercier, and S. Miryusupov, Monograph, to appear in the book series SIAM Data Science. Also available at ArXiv: https://arxiv.org/abs/2402.07084.
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, A class of kernel-based scalable algorithms for data science Also available at ArXiv: https://arxiv.org/abs/2410.14323.
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, Extrapolation and generative algorithms for three applications in finance, The Willmot Journal, September 2024, pp. 54–60. Available at. Also available at ArXiv: https://arxiv.org/abs/2404.13355. Journal (DOI)

 

2023

• B. Le Floch and P.G. LeFloch, Optimal localization for the Einstein constraints, ArXiv:2312.17706, 2023. Also available at ArXiv: https://arxiv.org/abs/2312.17706.
• P.G. LeFloch and T.-C. Nguyen, The seed-to-solution method for the Einstein constraints and the asymptotic localization problem, Jour. Funct. Anal. 285 (2023), 110106. Also available as ArXiv:1903.00243. Journal (DOI)
• P.G. LeFloch, J. Oliver, and Y. Tsutsumi, Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model, J. Evol. Equ. 23 (2023), 75. Journal (DOI)
• P.G. LeFloch and Y. Ma, Nonlinear stability of self-gravitating massive fields. A wave-Klein-Gordon model, Class. Quantum Grav. 40 (2023), 154001. Also available at ArXiv: https://arxiv.org/abs/2212.07463. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, Mesh-free algorithms for a class of problems arising in finance and machine learning, J. Sc. Comput. 95 (2023), 75. Also available at ArXiv: https://arxiv.org/abs/2304.10521. Journal (DOI)

 

2022

• P.G. LeFloch and Y. Ma, Einstein-Klein-Gordon spacetimes in the harmonic near-Minkowski regime, Port. Math. 79 (2022), 343–393. Also available at ArXiv: https://arxiv.org/abs/2208.08676. Journal (DOI)
• B. Le Floch, P.G. LeFloch, and G. Veneziano, Cyclic spacetimes through singularity scattering maps. Plane-symmetric gravitational collisions, Class. Quantum Grav. 39 (2022), 225010. Journal (DOI)
• B. Le Floch, P.G. LeFloch, and G. Veneziano, Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces, J. High Energy Phys. 04 (2022), 095. Journal (DOI)
• P.G. LeFloch, Gravitational singularities, scattering maps for bouncing, and structure-preserving algorithms, Proceedings of the Sixteenth Marcel Grossmann Meeting (MG16), Rome, Italy, 2021. Edited by G. Vereshchagin and R. Ruffini, World Scientific, 2022. See also ArXiv:2111.12650. Also available at ArXiv: https://arxiv.org/abs/2111.12650.
• E. Kardhashi, M. Laforest, and P.G. LeFloch, The mathematical theory of splitting-merging patterns in phase transition dynamics, Comm. Partial Differential Equations 47 (2022), 1339–1393. Also available at ArXiv: https://arxiv.org/abs/2105.06664. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, technical report, Predictive machines with uncertainty quantification, available at.
• P.G. LeFloch and and A.D. Tesdall, The positive entropy production property for augmented nonlinear hyperbolic models, Comptes Rendus Mathématiques 360 (2022), 35–46. Also available at ArXiv: https://arxiv.org/abs/1912.03563. Journal (DOI)
• Y.-Y. Cao, M.A. Ghazizadeh, and P.G. LeFloch, Asymptotic structure of cosmological fluid flows in one and two space dimensions: a numerical study, Commun. Appl. Math. Comput. Sci. 17 (2022), 79–129. Also available at ArXiv: https://arxiv.org/abs/1912.13439. Journal (DOI)

 

2021

• B. Boutin, F. Coquel, and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure, Networks Heter. Media 16 (2021), 283–315. [HAL]. Also available at HAL: https://hal.archives-ouvertes.fr/hal-02962629. Journal (DOI)
• S. Dong, P.G. LeFloch, and Z. Wyatt, Global evolution of the U(1) Higgs Boson: nonlinear stability and uniform energy bounds, Annals Henri Poincaré 22 (2021), 677–713. Also available at ArXiv: https://arxiv.org/abs/1902.02685.
• P.G. LeFloch and C.W. Wei, The global nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FRW geometry, Annals H. Poincaré, Nonlinear Analysis 38 (2021), 787–814. Also available at ArXiv: https://arxiv.org/abs/1512.03754.
• P.G. LeFloch, Singularity scattering laws for bouncing cosmologies: a brief overview, Proceedings of the 10th International Meeting on Lorentzian Geometry, Springer Verlag, 2022. A. L. Albujer et al. (eds.), Developments in Lorentzian Geometry, Springer Proceedings in Mathematics & Statistics 389. See also ArXiv:2106.07958. Also available at ArXiv: https://arxiv.org/abs/2106.07958.
• B. Le Floch, P.G. LeFloch, and G. Veneziano, Universal scattering laws for quiescent bouncing cosmology, Physical Rev. D. 8 (2021), 083531. Journal (DOI)
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, technical report, CodPy: a kernel-based ordering algorithm, available at.
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, technical report, CodPy: an advanced tutorial, available at.
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, technical report, CodPy: a tutorial, available at.
• P.G. LeFloch, C. Parés, and E. Pimentel-García, A class of well-balanced algorithms for relativistic fluids on a Schwarzschild background, Journal of Scientific Computing 89 (2021), 1–43. See also ArXiv:2011.07587. Journal (DOI)
• P.G. LeFloch and H. Ranocha, Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts, Jour. Scientific Comput. 87 (2021), 1–38. Also available at ArXiv: https://arxiv.org/abs/2007.08780. Journal (DOI)
• H. Karjoun, A. Beljadid, and P.G. LeFloch, A structure-preserving algorithm for surface water flows with transport processes, Adv. Comput. Math. 48 (2022), 7. Also available at ArXiv: https://arxiv.org/abs/2012.13702. Journal (DOI)
• F. Beyer and P.G. LeFloch, A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes, J. Comput. Phys. 431 (2021), 110145. Also available at ArXiv: https://arxiv.org/abs/2005.13504. Journal (DOI)
• Y.-Y. Cao, M.A. Ghazizadeh, and P.G. LeFloch, Asymptotic structure of cosmological Burgers flows in one and two space dimensions: a numerical study, Communications in Computational Physics 29 (2021), 472–509. Also available at ArXiv: https://arxiv.org/abs/1911.07239. Journal (DOI)

2020

• P.G. LeFloch, and W. Yan, Nonlinear stability of blow-up solutions to the Hyperbolic Mean Curvature flow, J. Differential Equations 269 (2020), 8269–8307. Journal (DOI)
• B. Le Floch and P.G. LeFloch, Compensated compactness and corrector stress tensor for the Einstein equations in T2 symmetry, Portugaliae Math. 77 (2020), 409–421. See also ArXiv:1912.12981. Also available at ArXiv: https://arxiv.org/abs/1912.12981. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions, Comput. Methods Appl. Mech. Engrg. 369 (2020), 113245. Also available at ArXiv: https://arxiv.org/abs/1911.00795. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, The Transport-based Mesh-free Method (TMM). A short review, The Wilmott journal 109 (2020), 52–57. Also available at ArXiv:1911.00992 and. Journal (DOI)
• J. Giesselman and P.G. LeFloch, Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary, Numerische Mathematik 144 (2020), 751–785. Journal (DOI)

 

2019

• B. Le Floch and P.G. LeFloch, On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry, Arch. Rational Mech. Anal. 233 (2019), 45–86. Also available at ArXiv: https://arxiv.org/abs/1805.10278. Journal (DOI)
• P.G. LeFloch and S. Xiang, Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime. II, J. Math. Pure Appl. 122 (2019), 272–317. Journal (DOI)
• S. Dong and P.G. LeFloch, Convergence of the finite volume method on a Schwarzschild background, ESAIM-M2AN (2019), 1459–1476. Also available at ArXiv: https://arxiv.org/abs/1901.10973.
• A. Beljadid, P.G. LeFloch, and M. Mohamadian, Late-time asymptotic behavior of solutions to hyperbolic conservation laws on the sphere, Comput. Methods Appl. Mech. Engrg. 349 (2019), 285–311. Journal (DOI)

2018

• P.G. LeFloch and C.-H. Wei, ., Boundedness of the total energy of relativistic membranes evolving in a curved spacetime, J. Differential Equations 265 (2018), 312–331. Journal (DOI)
• J.P. Dias and and P.G. LeFloch, A new approach to the Cauchy and Goursat problems for the nonlinear Wheeler-DeWitt equation, NoDEA (Nonlin. Differ. Equa. Appl.) 25 (2018), no. 2, Art. 10. Journal (DOI)
• P.G. LeFloch and S. Xiang, A numerical study of the relativistic Burgers and Euler equations on a Schwarzschild black hole exterior, Commun. Appl. Math. Comput. Sci. (CAMCOS) 13 (2018), 271–301.
• T. Ceylan, P.G. LeFloch, and B. Okutmustur, A finite volume method for the relativistic Burgers equation on a FLRW background spacetime, Commun. Comput. Phys. 23 (2018), 500–519.
• P.G. LeFloch, , The global nonlinear stability of Minkowski spacetime for self-gravitating massive fields, Springer Nature 2018, C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems II, Springer Proc. in Mathematics & Statistics, Vol. 237. Also available at ArXiv: https://arxiv.org/abs/1612.09421.
• Y. Bakhtin and P.G. LeFloch, Ergodicity of spherically symmetric fluid flows outside of a Schwarzschild black hole with random boundary forcing, Stoch PDE: Anal. Comp. 6 (2018), 746–785. Also available at ArXiv: https://arxiv.org/abs/1706.01004.

2017

• Q. Du, Z. Huang, and P.G. LeFloch, Nonlocal conservation laws. A new class of monotonicity-preserving models, SIAM J. Numer. Anal. 55 (2017), 2465–2489. Journal (DOI)
• P.G. LeFloch and Y. Ma, The mathematical validity of the f(R)-theory of modified gravity, Mém. Soc. Math. Fr. (N.S.) No. 150 (2017), 119 pp. Also available at ArXiv: https://arxiv.org/abs/1412.8151. Journal (DOI)
• P.G. LeFloch and Y. Ma, unpublished manuscript,, The Euclidian-hyperboidal foliation method and the nonlinear stability of Minkowski spacetime, ArXiv:1712.10048. Also available at ArXiv: https://arxiv.org/abs/1712.10048.
• P.G. LeFloch and Y. Ma, The global nonlinear stability of Minkowski space for self-gravitating massive fields, World Scientific Press, Singapore, August 2017 (188 pages).
• F. Beyer and P.G. LeFloch, Dynamics of self–gravitating fluids in Gowdy-symmetric spacetimes near cosmological singularities, Comm. Part. Diff. Equa. 42 (2017), 1199–1248. Also available at ArXiv: https://arxiv.org/abs/1512.07187.
• E. Ames, F. Beyer, J. Isenberg, and P.G. LeFloch, A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges, J. Geom. Phys. 121 (2017), 42–71. Also available at ArXiv: https://arxiv.org/abs/1602.03018. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, A new method for solving Kolmogorov equations in mathematical finance, C.R. Math. Acad. Sci. Paris 355 (2017), 680–686. Also available at ArXiv: https://arxiv.org/abs/1606.09612. Journal (DOI)
• A. Beljadid and P.G. LeFloch,, A central-upwind geometry-preserving method for hyperbolic conservation laws on the sphere, Commun. Appl. Math. Comput. Sci. 12 (2017), 81–107.
• A. Beljadid, P.G. LeFloch, S. Mishra, and C. Pares, Schemes with well-controlled dissipation. Hyperbolic systems in nonconservative form, Commun. in Comput. Phys. 21 (2017), 913–946.

2016

• J. Jang, P.G. LeFloch, and N. Masmoudi, Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum, J. Differential Equa. 260 (2016), 5481–5509. Journal (DOI)
• P. Germain and P.G. LeFloch, The finite energy method for compressible fluids: the Navier-Stokes-Korteweg model, Comm. Pure Appl. Math. 64 (2016), 3–61.
• P.G. LeFloch and S. Xiang, Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime, J. Math. Pures Appl. 106 (2016), 1038–1090. Also available at ArXiv: https://arxiv.org/abs/1512.08253. Journal (DOI)
• P.G. LeFloch and Y. Ma, The global nonlinear stability of Minkowski space for self-gravitating massive fields. The wave-Klein-Gordon model, Comm. Math. Phys. 346 (2016), 603–665. Also available at ArXiv: https://arxiv.org/abs/1507.01143. Journal (DOI)
• P.G. LeFloch and Y. Ma, The global nonlinear stability of Minkowski spacetime for the Einstein equations in presence of massive fields, Note C.R. Acad. Sc. Paris 354 (2016), 948–953. Also available at ArXiv: https://arxiv.org/abs/1507.02715. Journal (DOI)
• P.G. LeFloch and J. Smulevici, Future asymptotics and geodesic completeness of polarized T2-symmetric spacetimes, Annals and PDE 9 (2016), 363–395. Also available at ArXiv: https://arxiv.org/abs/1408.2084.
• P.G. LeFloch and J. Smulevici, Weakly regular T2-symmetric spacetimes. The future causal geometry of Gowdy spaces, J. Differ. Equa. 260 (2016), 1496–1521. Also available at ArXiv: https://arxiv.org/abs/1403.6252. Journal (DOI)

2015

• B. Boutin, F. Coquel, and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. IV. Well-balanced schemes for scalar multidimensional and multi-component laws, Math. Comp. 84 (2015), 1663–1702.
• D. Lee and P.G. LeFloch, The positive mass theorem for manifolds with distributional curvature, Comm. Math. Phys. 339 (2015), 99–120. Also available at ArXiv: https://arxiv.org/abs/1408.4431. Journal (DOI)
• P.G. LeFloch and C. Sormani, The nonlinear stability of rotationally symmetric spaces with low regularity, J. Funct. Anal. 268 (2015), 2005–2065. Also available at ArXiv: https://arxiv.org/abs/1401.6192. Journal (DOI)
• N. Grubic and P.G. LeFloch, On the area of the symmetry orbits in weakly regular Einstein-Euler spacetimes with Gowdy symmetry, SIAM J. Math. Anal. 47 (2015), 669–683. Also available at ArXiv: https://arxiv.org/abs/1411.3269.
• P.G. LeFloch and J. Smulevici, Weakly regular T2 symmetric spacetimes. The global geometry of future Cauchy developments, J. Eur. Math. Soc. 17 (2015), 1229–1292. Also available at ArXiv: https://arxiv.org/abs/1012.5931.
• A.P. Choudhury, K.T. Joseph, and P.G. LeFloch, The mathematical theory of self–similar boundary layers for nonlinear hyperbolic systems with viscosity and capillarity, Bull. Inst. Math. Acad. Sinica 10 (2015), 639–693.
• P.G. LeFloch and S. Xiang, Existence and uniqueness results for the pressureless Euler-Poisson system, Portugal Math. 72 (2015), 229–246.
• P.G. LeFloch and J.M. Mercier, Revisiting the method of characteristics via a convex hull algorithm, J. Comput. Phys. 298 (2015), 95–112. Also available at ArXiv: https://arxiv.org/abs/1409.0291.
• J. Ernest, P.G. LeFloch, and S. Mishra, Schemes with well-controlled dissipation (WCD), SIAM J. Numer. Anal. 53 (2015), 674–699.

2014

• N. Grubic, P.G. LeFloch, and C. Mardare, The equations of elastostatics in a Riemannian manifold, J. Math. Pures Appl. 102 (2014), 1121–1163.
• J.D.E. Grant and P.G. LeFloch, Null injectivity estimate under an upper bound on the curvature, Comm. Anal. Geom. 22 (2014), 965–996. Also available at ArXiv: https://arxiv.org/abs/1008.5167.
• A. Burtscher and P.G. LeFloch, The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation, J. Math. Pures Appl. 102 (2014), 1164–1217. Also available at ArXiv: https://arxiv.org/abs/1411.3008. Journal (DOI)
• R. Beig and P.G. LeFloch, Generalized relativistic hydrodynamics with a convex extension, Class. Quantum Grav. 31 (2014), 125005. Also available at ArXiv: https://arxiv.org/abs/1404.6403. Journal (DOI)
• P.G. LeFloch and Y. Ma, The hyperboloidal foliation method for nonlinear wave equations,, World Scientific Press, Singapore, 2014 (150 pages). Also available at ArXiv: https://arxiv.org/abs/1411.4910.
• P.G. LeFloch and H. Makhlof, A geometry-preserving finite volume method for compressible fluids on Schwarzschild spacetime, Commun. Comput. Phys. 15 (2014), 827–852. Also available at ArXiv: https://arxiv.org/abs/1212.6622. Journal (DOI)
• P.G. LeFloch and S. Mishra, Numerical methods with controled dissipation for small-scale dependent shocks, Acta Numer. 23 (2014), 743—-816. Also available at ArXiv: https://arxiv.org/abs/1312.1280.
• S. Boscarino, P.G. LeFloch, and G. Russo, High–order asymptotic preserving methods for fully nonlinear relaxation problems, SIAM J. Sci. Comput. 36 (2014), 377–395. Also available at ArXiv: https://arxiv.org/abs/1210.4761.
• P.G. LeFloch, Structure-preserving shock-capturing methods: late-time asymptotics, curved geometry, small-scale dissipation, and nonconservative products,, in “Lecture Notes of the XV Jacques-Louis Lions Spanish-French School”, Ed. C. Parès, C. Vázquez, and F. Coquel, Springer Verlag, Switzerland, 2014, pp. 179–222. Also available at ArXiv: https://arxiv.org/abs/1512.08181.

2013

• B. Boutin, F. Coquel, and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. III. The well–balanced approximation of thick interfaces, SIAM J. Numer. Anal. 51 (2013), 1108–1133.
• N. Grubic and P.G. LeFloch, Weakly regular Einstein–Euler spacetimes with Gowdy symmetry. The global areal foliation, Arch. Rational Mech. Anal. 208 (2013), 391–428. Also available at ArXiv: https://arxiv.org/abs/1212.1301.
• P.G. LeFloch, Hyperbolic balance laws with entropy on a curved spacetime. The weak-strong uniqueness theory, J. Hyperbolic Differ. Equ. 10 (2013), 773–798.
• P. Amorim, J.-P. Dias, M. Figueira, and P.G. LeFloch, The linear stability of shock waves for the nonlinear Schrödinger–inviscid Burgers system, J. Dyn. Diff. Equat. 25 (2013), 49–69.
• E. Ames, F. Beyer, J. Isenberg, and P.G. LeFloch, Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes, Ann. H. Poincaré 14 (2013), 1445–1523. Also available at ArXiv: https://arxiv.org/abs/1205.1881. Journal (DOI)
• E. Ames, Complex Analysis and Dynamical Systems V, F. Beyer, J. Isenberg, and P.G. LeFloch, Quasilinear symmetric hyperbolic Fuchsian systems in several space dimensions, Contemp. Math. 591 (2013), 1–19. Also available at ArXiv: https://arxiv.org/abs/1205.2166.
• P.G. LeFloch, A framework for late-time/stiff relaxation asymptotics, in “The Courant-Friedrichs-Lewy (CFL) condition”, Birkhäuser & Springer, New York, 2013, pp. 119–137.
• C. Berthon, P.G. LeFloch, and R. Turpault, Late-time/stiff-relaxation asymp\-totic-preserving approximations of hyperbolic equations, Math. of Comput. 82 (2013), 831–860.

2012

• P.G. LeFloch, H. Makhlof, and B. Okutmustur, Relativistic Burgers equations on curved spacetimes. Derivation and finite volume approximation, SIAM J. Numer. Anal. 50 (2012), 2136–2158. Also available at ArXiv: https://arxiv.org/abs/1206.3018.
• A. Burtscher, J.D.E. Grant, and P.G. LeFloch, New energy inequalities for tensorial wave equations on spacetimes that satisfy a one-sided bound, Comm. Partial Diff. Equations 37 (2012), 1596–1619.
• C. Berthon, F. Coquel, and P.G. LeFloch, Why many theories of shock waves are necessary. Kinetic relations for nonconservative systems, Proc. Royal Soc. Edinburgh 137 (2012), 1–37.

2011

• B. Boutin, F. Coquel, and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. I. Self-similar diffusion for thin interfaces, Proc. Royal Soc. Edinburgh 141A (2011), 921–956.
• P.G. LeFloch, Einstein spacetimes with weak regularity, in “Advances in Lorentzian Geometry”, Ed. M. Plaue, A.D. Rendall, and M. Scherfner, AMS/IP series, Vol. 49, 2011, pp. 81–96. Also available at ArXiv: https://arxiv.org/abs/1009.1884.
• P.G. LeFloch, Existence of CMC–harmonic coordinates for spacetimes with bounded curvature, Sémin. Théor. Spectr. Géom. (2011), Grenoble.
• P.G. LeFloch and B.S. Tchapnda, Plane-symmetric spacetimes with positive cosmological constant. The case of stiff fluids, Adv. Theor. Math. Phys. 15 (2011), 1–26. Also available at ArXiv: https://arxiv.org/abs/1011.4571.
• P.G. LeFloch and A.D. Rendall, A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3, Arch. Rational Mech. Anal. 201 (2011), 841–870. Also available at ArXiv: https://arxiv.org/abs/1004.0427. Journal (DOI)
• P.G. LeFloch, Hyperbolic conservation laws on spacetimes, in “Nonlinear conservation laws and applications”, IMA Vol. Math. Appl. 153, Springer, New York, 2011, pp. 379–391. Also available at ArXiv: https://arxiv.org/abs/1006.2439.
• P.G. LeFloch and J.M. Stewart, The characteristic initial value problem for plane–symmetric spacetimes with weak regularity, Class. Quantum Grav. 28 (2011), 145019–145035. Also available at ArXiv: https://arxiv.org/abs/1004.2343.
• P.G. LeFloch and M.-D. Thanh, A Godunov-type method for the shallow water equations with variable topography in the resonant regime, J. Comput. Phys. 230 (2011), 7631–7660.
• F. Beyer and P.G. LeFloch, Second–order hyperbolic Fuchsian systems. Asymptotic behavior of geodesics in Gowdy spacetimes, Phys. Rev. D. 84 (2011), 084036. Also available at ArXiv: https://arxiv.org/abs/1108.4718.
• P. Amorim, P.G. LeFloch, and W. Neves, A geometric approach to error estimates for conservation laws posed on a spacetime, Nonlinear Anal. TMA 74 (2011), 4898–4917. Also available at ArXiv: https://arxiv.org/abs/1002.3137.

2010

• P.G. LeFloch, Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues,, Lectures given at Centre for Advanced Study of the Norwegian Academy of Science and Letters, Oslo, Norway, Contemporary Mathematics, vol. 526, Amer. Math. Soc., Providence, RI, 2010, pp. 237–272. Also available at ArXiv: https://arxiv.org/abs/1002.2950.
• N. Bedjaoui, P.G. LeFloch, J. Martin-Garcia, and J. Novak, Existence of naked singularities for the Brans-Dicke theory. An analytical and numerical study, Class. Quantum Grav. 27 (2010), 245010. Also available at ArXiv: https://arxiv.org/abs/1008.4238.
• F. Beyer and P.G. LeFloch, Second–order hyperbolic Fuchsian systems and applications, Class. Quantum Grav. 27 (2010), 245012–245033. Also available at ArXiv: https://arxiv.org/abs/1011.0270.
• F. Beyer and P.G. LeFloch, (unpublished)., Second-order hyperbolic Fuchsian systems. II. Gowdy spacetimes and the Fuchsian numerical algorithm, ArXiv:1006.2525. Also available at ArXiv: https://arxiv.org/abs/1006.2525.
• F. Beyer and P.G. LeFloch, (unpublished)., Second-order hyperbolic Fuchsian systems. I. General theory, ArXiv:1004.4885. Also available at ArXiv: https://arxiv.org/abs/1004.4885.
• P.G. LeFloch and J. Smulevici, Global geometry of T2 symmetric spacetimes with weak regularity, Note C.R. Acad. Sc. 348 (2010), 1231–1233. Also available at ArXiv: https://arxiv.org/abs/1006.2933. Journal (DOI)
• M. Laforest and P.G. LeFloch, Diminishing functionals for nonclassical entropy solutions selected by kinetic relations, Portugal Math. 67 (2010), 279–319. Also available at ArXiv: https://arxiv.org/abs/0812.4021.

2009

• P.G. LeFloch and S. Mishra, Kinetic functions in magnetohydrodynamics with resistivity and Hall effects, Acta Math. Scientia 29B (2009), 1684–1702.
• P.G. LeFloch, C. Mardare, and S. Mardare, Isometric immersions into the Minkow\-ski spacetime for Lorentzian manifolds with limited regularity, Disc. Cont. Dyn. Syst. 23 (2009), 341–365. Also available at ArXiv: https://arxiv.org/abs/0712.4214.
• B.-L. Chen and P.G. LeFloch, Local foliations and optimal regularity of Einstein spacetimes, J. Geom. Phys. 59 (2009), 913–941. Also available at ArXiv: https://arxiv.org/abs/0812.5053. Journal (DOI)
• P.G. LeFloch, Local canonical foliations of Lorentzian manifolds with bounded curvature, in “Geometry, Topology, Quantum Fields Theories, and Cosmology”, J. Kouneiher, C. Barbachoux & F. Hélein eds., Edition Hermann Sciences, 2009. Also available at ArXiv: https://arxiv.org/abs/0812.3960.
• P.G. LeFloch, Injectivity radius and optimal regularity for Lorentzian manifolds with bounded curvature, Sémin. Théor. Spectr. Géom. 26 (2009), 77–90. Also available at ArXiv: https://arxiv.org/abs/0812.2671.
• P.G. LeFloch, Einstein-Euler equations for matter spacetimes with Gowdy symmetry, Sémi\-naire X-EDP, Ecole Polytechnique, Palaiseau, 2009.
• P.G. LeFloch and S. Ukai, A symmetrization of the relativistic Euler equations in several spatial variables, Kinetic & Related Models 2 (2009), 275–292. Also available at ArXiv: https://arxiv.org/abs/0812.4001.
• S. Georgiev and P.G. LeFloch, Generalized time-periodic solutions to the Euler equations of compressible fluids, Different. Equa. Appl. (DEA) 1 (2009), 413–426.
• P.G. LeFloch and M. Yamazaki, The dynamics of isothermal relativistic fluids, in Proc. of the RIMS Workshop on “Hyperfunctions and Linear Partial Differential Equations”, Kyoto, June 2006, Research Institute for Mathematical Sciences (RIMS), Sûrikaisekiken kyûsho Kôkyûroku No. 1648 (2009), 117–132.
• P.G. LeFloch, Stability in the L1 norm via a linearization method for nonlinear hyperbolic systems, Proceedings of Hyp2008, 12th International Conference on Hyperbolic Problems, University of Maryland, College Park, June 2008, 2009. Also available at ArXiv: https://arxiv.org/abs/0812.3999.
• P.G. LeFloch, Existence and qualitative properties of kinetic functions generated by diffusive-dispersive regularizations, Contemp. Mat. 37 (2009), 43–89. Also available at ArXiv: https://arxiv.org/abs/1005.2479.
• F. Kissling, P.G. LeFloch, and C. Rohde, A kinetic decomposition for singular limits of non-local conservation laws, J. Differential Equations 247 (2009), 3338–3356.
• M. Ben-Artzi, J. Falcovitz, and P.G. LeFloch, Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme, J. Comput. Phys. 228 (2009), 5650–5668. Also available at ArXiv: https://arxiv.org/abs/0808.2062.
• M.J. Castro, P.G. LeFloch, M.L. Munoz-Ruiz, and C. Pares, Numerical investigation of finite difference schemes for nonconservative hyperbolic systems, in “Hyperbolic problems: theory, numerics and applications”, Proc. Sympos. Appl. Math., 67, Part 2, Amer. Math. Soc., Providence, RI, 2009, pp. 465–475.
• P. Amorim, C. Bernardi, and P.G. LeFloch, Computing Gowdy spacetimes via spectral evolution in future and past directions, Class. Quantum Grav. 26 (2009), 1–18. Also available at ArXiv: https://arxiv.org/abs/0811.1266. Journal (DOI)
• P.G. LeFloch, W. Neves, and B. Okutmustur, Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes, Acta Math. Sinica 25 (2009), 1041–1066.

2008

• R.M. Colombo, Hyperbolic aspects of phase transition dynamics, D. Kröner and P.G. LeFloch, Abstracts from the mini-workshop held February 24–March 1, 2008, Oberwolfach Rep. 5 (2008), 513–556.
• A. Ambroso, B. Boutin, F. Coquel, E. Godlewski, and P.G. LeFloch, Coupling two scalar conservation laws via Dafermos self-similar regularization, Proc. ENUMATH 2007, 7th European Conf. on Numer. Math. Adv. Appl., Springer Verlag, Heidelberg, 2008, pp. 209–216.
• P.G. LeFloch and K. Smoczyk, The hyperbolic mean curvature flow, J. Math. Pures Appl. 90 (2008), 591–614. Also available at ArXiv: https://arxiv.org/abs/0712.0091.
• B.-L. Chen and P.G. LeFloch, Injectivity radius estimates for Lorentzian manifolds, Commun. Math. Phys. 278 (2008), 679–713. Also available at ArXiv: https://arxiv.org/abs/math/0612860. Journal (DOI)
• P. Amorim and P.G. LeFloch, Sharp estimates for periodic solutions to the Euler–Poisson–Darboux equation, Portugal Math. 65 (2008), 387–429.
• L. Ambrosio, G. Crippa, and P.G. LeFloch, Leaf superposition property for integer rectifiable currents, Netw. Heterog. Media 3 (2008), 85–95.
• P.G. LeFloch and B. Okutmustur, Hyperbolic conservation laws on manifolds with limited regularity, C.R. Math. Acad. Sc. Paris 346 (2008), 539–543. Also available at ArXiv: https://arxiv.org/abs/0808.2895.
• M.J. Castro, P.G. LeFloch, M.L. Munoz-Ruiz, and C. Pares, Why many theories of shock waves are necessary. Convergence error in formally path-consistent schemes, J. Comput. Phys. 227 (2008), 8107–8129. Also available at ArXiv: https://arxiv.org/abs/0808.2065.
• P.G. LeFloch and M. Mohamadian, Why many shock wave theories are necessary. Fourth-order models, kinetic functions, and equivalent equations, J. Comput. Phys. 227 (2008), 4162–4189. Also available at ArXiv: https://arxiv.org/abs/0712.3810.
• D. Kröner, P.G. LeFloch, and M.D. Thanh, The minimum entropy principle for fluid flows in a nozzle with discontinuous cross-section, Math. Meth. Appl. Sc. (M2AN) 42 (2008), 425–442.
• B. Boutin, C. Chalons, F. Lagoutière, and P.G. LeFloch, Convergent and conservative schemes for nonclassical solutions based on kinetic relations, Interfaces and Free Boundaries 10 (2008), 399–421.
• P. Amorim, P.G. LeFloch, and B. Okutmustur, Finite volume schemes on Lorentzian manifolds, Comm. Math. Sc. 6 (2008), 1059–1086.
• P.G. LeFloch and B. Okutmustur, Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms, Far East J. Math. Sci. 31 (2008), 49–83. Also available at ArXiv: https://arxiv.org/abs/0810.0255.

2007

• P.G. LeFloch and M. Yamazaki, Entropy solutions of the Euler equations for isothermal relativistic fluids, Intern. J. Dynamical Syst. Differential Equa. 1 (2007), 20–37. Also available at ArXiv: https://arxiv.org/abs/math/0701042.
• P.G. LeFloch and M. Westdickenberg, Finite energy solutions of the isentropic Euler equations, J. Math. Pures Appl. 88 (2007), 389–429. Also available at ArXiv: https://arxiv.org/abs/0812.2688.
• M. Ben-Artzi and P.G. LeFloch, The well-posedness theory for geometry compatible hyperbolic conservation laws on manifolds, Ann. Inst. Henri Poincaré — Nonlinear Analysis 24 (2007), 989—1008. Also available at ArXiv: https://arxiv.org/abs/math/0612846.
• P.G. LeFloch and C. Mardare, Definition and weak stability of spacetimes with distributional curvature, Portugal Math. 64 (2007), 535–573. Also available at ArXiv: https://arxiv.org/abs/0712.0122.
• O. Glass and P.G. LeFloch, Nonlinear hyperbolic systems : Non-degenerate flux, inner speed variation, and graph solutions, Arch. Rational Mech. Anal. 185 (2007), 409–480. Also available at ArXiv: https://arxiv.org/abs/math/0701041.
• J. Hong and P.G. LeFloch, A version of the Glimm method based on generalized Riemann problems, Portugal Math. 64 (2007), 199–236. Also available at ArXiv: https://arxiv.org/abs/math/0701063.
• K.T. Joseph and P.G. LeFloch, Singular limits for the Riemann problem: general diffusion, relaxation, and boundary conditions, C.R. Math. Acad. Sci. Paris 344 (2007), 59–64. Also available at ArXiv: https://arxiv.org/abs/0812.2680.
• K.T. Joseph and P.G. LeFloch, Singular limits in phase dynamics with physical viscosity and capillarity, Proc. Royal Soc. Edinburgh 137A (2007), 1287–1312. Also available at ArXiv: https://arxiv.org/abs/math/0701007.
• P.G. LeFloch and M.D. Thanh, The Riemann problem for the shallow water equations with discontinuous topography, Comm. Math. Sci. 5 (2007), 865–885. Also available at ArXiv: https://arxiv.org/abs/0712.3778.
• B. Boutin, C. Chalons, F. Lagoutière and P.G. LeFloch, A sharp interface and fully conservative scheme for computing nonclassical shocks, in “Numerical Mathematics and Advanced Applications”, Proc. ENUMATH 2007, 7th European Conf. on Numer. Math. Adv. Appl., Graz, Austria, September 2007, Springer Verlag, Heidelberg, K. Kunisch, G. Of, and O. Steinbach (Eds.), 2008, pp. 217–224.

2006

• P.G. LeFloch, Haar method, averaged matrix, wave cancellation, and L1 stability for hyperbolic systems, J. Hyperbolic Differ. Equ. 3 (2006), 701–739. Also available at ArXiv: https://arxiv.org/abs/0812.2685.
• P.G. LeFloch and H. Frid, Uniqueness for multidimensional hyperbolic systems with commuting Jacobians, Arch. Rational Mech. Anal. 182 (2006), 25–47.
• K.T. Joseph and P.G. LeFloch, Singular limits for the Riemann problem. General diffusion, relaxation, and boundary conditions, in “New analytical approach to multidimensional balance laws”, O. Rozanova ed., Nova Press, 2006, pp. 143–172.

2005

• P.G. LeFloch and J.M. Stewart, Shock waves and gravitational waves in matter spacetimes with Gowdy symmetry, Portugal. Math. 62 (2005), 349–370.
• P.G. LeFloch and V. Shelukhin, Symmetries and global solvability of the isothermal gas dynamics equations, Arch. Rational Mech. Anal. 175 (2005), 389–430. Also available at ArXiv: https://arxiv.org/abs/math/0701100.
• N. Bedjaoui, C. Chalons, F. Coquel, and P.G. LeFloch, Non-monotonic traveling waves in Van der Waals fluids, Analysis Appl. 3 (2005), 419–446.
• P. Amorim, M. Ben-Artzi, and P.G. LeFloch, Hyperbolic conservation laws on manifolds: Total variation estimates and finite volume method, Meth. Appl. Analysis 12 (2005), 291–324. Also available at ArXiv: https://arxiv.org/abs/math/0612847.

2004

• P.G. LeFloch and V. Shelukhin, Symmetries and global solvability of the Cauchy problem for equations of the gas dynamics of isothermal flows, Doklady Math. Sc. 398 (2004), 300–305.
• P.G. LeFloch, Graph solutions of nonlinear hyperbolic systems, J. Hyperbolic Differ. Equ. 1 (2004), 643–689.
• P.G. LeFloch and K. Trivisa, Continuous Glimm-type functionals and spreading of rarefaction waves, Comm. Math. Sci. 2 (2004), 213–236.
• N. Bedjaoui, C. Klingenberg, and P.G. LeFloch, On the validity of the Chapman-Enskog expansion for shock waves with small strength, Portugal. Math. 61 (2004). 479–499. Also available at ArXiv: https://arxiv.org/abs/0812.3985.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. V. Singular diffusion and dispersion terms, Proc. Royal Soc. Edinburgh 134A (2004), 815–844.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. IV. Compressible Euler system, Chinese Ann. Appl. Math. 24 (2003), 17–34.
• P.G. LeFloch and M. Shearer, Nonclassical Riemann solvers with nucleation, Proc. Royal Soc. Edinburgh 134A (2004), 941–964.
• P. Baiti, P.G. LeFloch, and B. Piccoli, Existence theory for nonclassical entropy solutions: scalar conservation laws, Z. Angew. Math. Phys. 55 (2004), 927–945.
• A.P. Barnes, P.G. LeFloch, B.G. Schmidt, and J.M. Stewart, The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes, Class. Quantum Grav. 21 (2004), 5043–5074.
• P. Goatin and P.G. LeFloch, The Riemann problem for a class of resonant nonlinear systems of balance laws, Ann. Inst. H. Poincaré – Analyse Non-linéaire 21 (2004), 881–902.

2003

• G.-Q. Chen and P.G. LeFloch, Existence theory for the compressible isentropic Euler equations, Arch. Rational Mech. Anal. 166 (2003), 81–98.
• T. Iguchi and P.G. LeFloch, Existence theory for hyperbolic systems of conservation laws with general flux-functions, Arch. Rational Mech. Anal. 168 (2003), 165–244.
• P. Goatin and P.G. LeFloch, L1 continuous dependence of entropy solutions for the compressible Euler equations, Comm. Pure Appl. Anal. 2 (2003), 107–137.
• P.G. LeFloch and M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section, Comm. Math. Sci. 1 (2003), 763–796.
• C. Chalons and P.G. LeFloch, Computing undercompressive waves with the random choice scheme. Nonclassical shock waves, Interfaces and Free Boundaries 5 (2003), 129–158.
• P.G. LeFloch and M.D. Thanh, Properties of Rankine-Hugoniot curves for Van der Waals fluids, Japan J. Indust. Applied Math. 20 (2003), 211–238.

2002

• P.G. LeFloch, Hyperbolic Systems of Conservation Laws. The theory of classical and nonclassical shock waves, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2002 (300 pages).
• J.-P. Dias and P.G. LeFloch, Some existence results on conservation laws with source-term, Math. Meth. Appl. Sc. 25 (2002), 1149–1160.
• G. Crasta and P.G. LeFloch, A class of nonconservative and non strictly hyperbolic systems, Comm. Pure Appl. Anal. 1 (2002), 513–530.
• K.T. Joseph and P.G. LeFloch, Boundary layers in weak solutions of hyperbolic conservation laws. III. Vanishing relaxation limits, Portugal. Math. 59 (2002), 453.
• K.T. Joseph and P.G. LeFloch, Boundary layers in weak solutions of hyperbolic conservation laws. II. Self-similar vanishing diffusion limits, Comm. Pure Appl. Anal. 1 (2002), 51–76.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. II. An hyperbolic-elliptic model of phase transitions, Proc. Royal Soc. Edinburgh 132 (2002), 545–565.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. I. Nonconvex hyperbolic conservation laws, J. Differential Equations 178 (2002), 574–607.
• C. Kondo and P.G. LeFloch, Zero diffusion-dispersion limits for hyperbolic conservation laws, SIAM Math. Anal. 33 (2002), 1320–1329. Also available at ArXiv: https://arxiv.org/abs/0712.0094.
• P.G. LeFloch, J.-M. Mercier, and C. Rohde, Fully discrete entropy conservative schemes of arbitrary order, SIAM J. Numer. Anal. 40 (2002), 1968–1992.
• J.M. Correia, P.G. LeFloch, and M.D. Thanh, Hyperbolic conservation laws with Lipschitz continuous flux-functions. The Riemann problem, Bol. Soc. Bras. Mat. 32 (2001), 271–301.

2001

• P. Goatin and P.G. LeFloch, Sharp L1 continuous dependence of solutions of bounded variation for hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 157 (2001), 35–73.
• P. Goatin and P.G. LeFloch, Sharp L1 stability estimates for hyperbolic conservation laws, Portugal Math. 58 (2001), 1–44. Also available at ArXiv: https://arxiv.org/abs/math/0006109.
• C. Kondo and P.G. LeFloch, Measure-valued solutions and well-posedness of multi-dimen\-sional conservation laws in a bounded domain, Portugal Math. 58 (2001), 171–194.
• P. Baiti, P.G. LeFloch, and B. Piccoli, Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems, J. Differential Equations 172 (2001), 59–82.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. III. An hyperbolic model of nonlinear elastodynamics, Ann. Univ. Ferrara Sc. Mat. 47 (2001), 117–144.
• P.G. LeFloch and C. Rohde, The zero diffusion-dispersion limit for the Riemann problem, Indiana Univ. Math. J. 50 (2001), 1707–1743.
• C. Chalons and P.G. LeFloch, High-order entropy conservative schemes and kinetic relations for van der Waals fluids, J. Comput. Phys. 167 (2001), 1–23.
• G.-Q. Chen and P.G. LeFloch, Entropies and entropy-flux splittings for the isentropic Euler equations, Chinese Annal. Math. 22 (2001), 1–14.
• C. Chalons and P.G. LeFloch, A fully discrete scheme for diffusive-dispersive conservation laws, Numerische Math. 89 (2001), 493–509.
• P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations I. A nonconvex hyperbolic model of phase transitions, Z. Angew. Math. Phys. 52 (2001), 597–619.
• P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase transitions, Proc. Royal Soc. Edinburgh 132A (2001), 181–219.

2000

• G.-Q. Chen and P.G. LeFloch, Compressible Euler equations with general pressure law, Arch. Rational Mech Anal. 153 (2000), 221–259.
• J. Hu and P.G. LeFloch, L1 continuous dependence property for systems of conservation laws, Arch. Rational Mech. Anal. 151 (2000), 45–93.
• P. Baiti, P.G. LeFloch, and B. Piccoli, BV Stability via generalized characteristics for nonclassical solutions of conservation laws, EQUADIFF’99, Proc. Internat. Conf. Differ. Equ., Berlin, August 1999, B. Fiedler, K. Gröger, and J.Sprekels, editors, World Sc. Publ., River Edge, NY, 2000, pp. 289–294.
• B.T. Hayes and P.G. LeFloch, Nonclassical shock waves and kinetic relations. Strictly hyperbolic systems, SIAM J. Math. Anal. 31 (2000), 941–991. (First appeared as : \# 357, CMAP, Ecole Polytechnique (France), November 1996.).
• P.G. LeFloch and C. Rohde, High-order schemes, entropy inequalities, and nonclassical shocks , SIAM J. Numer. Anal. 37 (2000), 2023–2060.
• P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations. III. A nonconvex hyperbolic model for Van der Waals fluids, Electr. J. Diff. Equa. 72 (2000), 1–19.

1999

• P.G. LeFloch, An introduction to nonclassical shocks of systems of conservation laws, International School on Hyperbolic Problems, Freiburg, Germany, Oct. 97, D. Kröner, Russo M. Ohlberger and C. Rohde eds., Lect. Notes Comput. Eng., Vol. 5, Springer Verlag, 1999, pp. 28–72.
• A. Bressan and P.G. LeFloch, Structural stability and regularity of entropy solutions to systems of conservation laws, Indiana Univ. Math. J. 48 (1999), 43–84.
• P.G. LeFloch and A. Tzavaras, Representation of weak limits and definition of nonconservative products, SIAM J. Math. Anal. 30 (1999), 1309–1342.
• K.T. Joseph and P.G. LeFloch, Boundary layers in weak solutions to hyperbolic conservation laws, Arch. Rational Mech Anal. 147 (1999), 47–88. (First appeared as: \# 341, CMAP, Ecole Polytechnique (France), November 1996.). Also available at ArXiv: https://arxiv.org/abs/math/0702024.
• P. Baiti, P.G. LeFloch, and B. Piccoli, Nonclassical shocks and the Cauchy problem. General conservation laws, Contemporary Math. 238 (1999), 1–25.
• D. Amadori, P. Baiti, P.G. LeFloch and B. Piccoli, Nonclassical shocks and the Cauchy problem for nonconvex conservation laws, J. Differential Equations 151 (1999), 345–372.
• P.G. LeFloch and R. Natalini, Conservation laws with vanishing nonlinear diffusion and dispersion, Nonlinear Analysis 36 (1999), 213–230. Also available at ArXiv: https://arxiv.org/abs/0711.0411.
• J.M. Correia and P.G. LeFloch, Nonlinear hyperbolic conservation laws, in “Nonlinear evolution equations and their applications” (Macau, 1998), World Sci. Publ., River Edge, NJ, 1999, pp. 21–44.
• T.Y. Hou, P. Rosakis, and P.G. LeFloch, A level set approach to the computation of twinning and phase transition dynamics, J. Comput. Phys. 150 (1999), 302–331.
• P.G. LeFloch and J.-G. Liu, Generalized monotone schemes, extremum paths and discrete entropy conditions, Math. of Comput. 68 (1999), 1025–1055. Also available at ArXiv: https://arxiv.org/abs/0711.0406.

1998

• J.M. Correia and P.G. LeFloch, Nonlinear diffusive-dispersive limits for multidimensional conservation laws, in “Advances in Nonlinear P.D.E.’s and Related Areas”, (Beijing, 1997), World Sci. Publ., River Edge, NJ, 1998, pp. 103–123. Also available at ArXiv: https://arxiv.org/abs/0810.1880.
• P.G. LeFloch, An entropy diminishing criterion for hyperbolic conservation laws, in “Numerical methods for wave propagation” (Manchester, 1995), Fluid Mech. Appl. 47, Kluwer Acad. Publ., Dordrecht, 1998, pp. 275–295.
• B.T. Hayes and P.G. LeFloch, Nonclassical shocks and kinetic relations. Finite difference schemes, SIAM J. Numer. Anal. 35 (1998), 2169–2194.
• P.G. LeFloch, Dynamics of solid-solid phase interfaces via a level set approach, Proc. Fifth Workshop on Partial Differential Equations (Rio de Janeiro, 1997), Mat. Contemp. 15 (1998), pp. 187–212.

1997

• G.-Q. Chen and P.G. LeFloch, Entropies and weak solutions to the isentropic compressible Euler equations, C.R. Math. Acad. Sc. Paris 324 (1997), 1105–1110.
• F. Bereux, E. Bonnetier, and P.G. LeFloch, Gas dynamics equations. Two special cases, SIAM J. Math. Anal. 28 (1997), 499–515.
• A. Bressan and P.G. LeFloch, Uniqueness of weak solutions to system of conservation laws, Arch. Rational Mech. Anal. 140 (1997), 301–331.
• B.T. Hayes and P.G. LeFloch, Nonclassical shocks and kinetic relations. Scalar conservation laws, Arch. Rational Mech. Anal. 139 (1997), 1–56.

1996

• B.T. Hayes and P.G. LeFloch, Measure-solutions to a strictly hyperbolic system of conservation laws, Nonlinearity 9 (1996), 1547–1563.
• P.G. LeFloch and A. Tzavaras, Existence theory for the Riemann problem for non-conservative hyperbolic systems, C.R. Acad. Sc. Paris, Série 1, 323 (1996), 347–352.
• P.G. LeFloch, Computational Methods for propagating phase boundaries, in “Intergranular and Interphase Boundaries in Materials : iib95”, Lisbon, June 1995, Eds. A.C. Ferro, J.P. Conde and M.A. Fortes. Material Science Forum Vols. 207–209, 1996, pp. 509–515.
• X.-G. Zhong, T.Y. Hou, and P.G. LeFloch, Computational methods for propagating phase boundaries, J. Comput. Phys. 124 (1996), 192–216.
• F. Coquel and P.G. LeFloch, An entropy satisfying MUSCL scheme for systems of conservation laws, Numer. Math. 74 (1996), 1–33.

1995

• G. Dal Maso, P.G. LeFloch, and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl. 74 (1995), 483–548.
• G.-Q. Chen and P.G. LeFloch, Entropy flux splittings for hyperbolic conservation laws. General framework, Comm. Pure Appl. Math. 48 (1995), 691–729.
• F. Coquel and P.G. LeFloch, An entropy satisfying second order scheme for systems of conservation laws, C.R. Acad. Sc. Paris, Série 1, 320 (1995), 1263–1268.
• B. Cockburn, F. Coquel, and P.G. LeFloch, Convergence of finite volume methods for multidimensional conservation laws, SIAM J. Numer. Anal. 32 (1995), 687–705.
• P.G. LeFloch, Monotonicity consistent scheme for hyperbolic conservation laws, Proc. “Fifth International Colloquium on Numerical Analysis”, Plovdiv, August 1995, ed. D. Bainov.

1994

• T.Y. Hou and P.G. LeFloch, Why nonconservative schemes converge to wrong solutions. Error analysis, Math. of Comput. 62 (1994), 497–530.
• B. Cockburn, F. Coquel, and P.G. LeFloch, Error estimates for finite volume methods for multidimensional conservation laws, Math. of Comput. 63 (1994), 77–103. (First appeared as: 91-20, AHCRC Institute, Minneapolis, USA, 1991.).
• P.G. LeFloch and J.-G. Liu, Discrete entropy and monotonicity criterion for hyperbolic conservation laws, C.R. Acad. Sc. Paris, Série I, 319 (1994), 881–886.

1993

• P.G. LeFloch, Propagating phase boundaries. Formulation of the problem and existence via the Glimm scheme, Arch. Rational Mech. Anal. 123 (1993), 153–197. Also available at ArXiv: https://arxiv.org/abs/math/0701646.
• P.G. LeFloch and Z.P. Xin, (unpublished)., Formation of singularities in periodic solutions to gas dynamics equations, \# 287, CMAP, Ecole Polytechnique (France), October 1993.
• P.G. LeFloch and Z.-P. Xin, Uniqueness via the adjoint problems for systems of conservation laws, Comm. Pure Appl. Math. 46 (1993), 1499–1533.
• P.G. LeFloch and T.-P. Liu, Existence theory for nonlinear hyperbolic systems in nonconservative form, Forum Math. 5 (1993), 261–280.
• G.-Q. Chen and P.G. LeFloch, Entropy flux-splittings for hyperbolic conservation laws, C.R. Acad. Sc. Paris, Série 1, 317 (1993), 761–766.
• F. Coquel and P.G. LeFloch, Convergence of finite difference schemes for scalar conservation laws in several space variables. General theory, SIAM J. Numer. Anal. 30 (1993), 675–700.

1992

• A. Forestier and P.G. LeFloch, Multivalued solutions to some nonlinear and nonstrictly hyperbolic systems, Japan J. Indus. Appl. Math. 9 (1992), 1–23.

1991

• P.G. LeFloch and T.-T. Li, A global in time asymptotic expansion for the solution of the generalized Riemann problem, Asymp. Analysis 3 (1991), 321-340.
• F. Coquel and P.G. LeFloch, Convergence of finite difference schemes for scalar conservation laws in several space variables. The corrected antidiffusive-flux approach, Math. of Comput. 57 (1991), 169–210.

1990

• P.G. LeFloch and F. Olsson, A second-order Godunov method for the conservation laws of nonlinear elastodynamics, Impact Comp. Sc. Eng. 2 (1990), 318–354.
• P.G. LeFloch, (unpublished)., On some nonlinear hyperbolic problems, Memoir of “Habilitation à Diriger des Recherches”, Université Pierre et Marie Curie (Paris 6), July 1990.
• P.G. LeFloch, An existence and uniqueness result for two nonstrictly hyperbolic systems, IMA Volumes in Math. and its Appl.,“Nonlinear evolution equations that change type”, ed. B.L. Keyfitz and M. Shearer, Springer Verlag, Vol. 27, 1990, pp. 126–138.
• F. Coquel and P.G. LeFloch, Convergence of finite difference schemes for conservation laws in several space dimensions, C.R. Acad. Sc. Paris, Série 1, 310 (1990), 455–460.

1989

• P.G. LeFloch, Existence of entropy solutions for the compressible Euler equations, Conf. on “Hyperbolic Problems: theory, numerics, and applications” (Zürich, 1998), International Series Numer. Math. Vol. 130, Birkäuser Verlag Bäsel, Switzerland, 1999, pp. 599–607.
• P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems in conservative form, Proc. Intern. Conf. on Hyperbolic problems, ed. J. Ballmann and R. Jeltsch, Notes on Num. Fluid Mech., Vol. 24, Viewieg, Braunschweig, 1989, pp. 362–373.
• P.G. LeFloch, (unpublished)., Shock waves for nonlinear hyperbolic systems in nonconservative form, Institute for Math. and its Appl., Minneapolis, IMA, \# 593, 1989 Available at:.
• F. Dubois and P.G. LeFloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, Proc. Inter. Conf. on Hyperbolic problems, Aachen (Germany), March 1988, Notes on Numer. Fluid Mech., Vol. 24, Vieweg, 1989, pp. 96-106.
• A. Bourgeade, P.G. LeFloch, and P.-A. Raviart, An asymptotic expansion for the solution of the generalized Riemann problem. Part II. Application to the gas dynamics equations, Ann. Inst. H. Poincaré, Nonlin. Anal. 6 (1989), 437-480.
• P.G. LeFloch and T.-T. Li, A global in time asymptotic expansion for the solution of the generalized Riemann problem, C.R. Acad. Sc. Paris, Série 1, 309 (1989), 807–810.

1988

• P.G. LeFloch, (unpublished)., Theory and numerical approximation of nonlinear hyperbolic systems, Ph.D. Memoir in Applied Mathematics, Ecole Polytechnique, Palaiseau, France, January 1988..
• P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems in nonconservative form, Comm. Part. Diff. Equa. 13 (1988), 669–727.
• P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems in nonconservative form, C.R. Acad. Sc. Paris, Série 1, 306 (1988), 181–186.
• F. Dubois and P.G. LeFloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations 71 (1988), 93–122.
• P.G. LeFloch and J.-C. Nédélec, Asymptotic time-behavior for weighted scalar nonlinear conservation laws, RAIRO: Math. Model. Num. Anal. 22 (1988), 469–475.
• P.G. LeFloch and J.-C. Nédélec, Explicit formula for weighted scalar nonlinear conservation laws, Trans. Amer. Math. Soc. 308 (1988), 667–683.
• P.G. LeFloch, Explicit formula for scalar conservation laws with boundary condition, Math. Meth. Appl. Sc. 10 (1988), 265–287.
• P.G. LeFloch and P.-A. Raviart, An asymptotic expansion for the solution of the generalized Riemann problem. Part I. General theory, Ann. Inst. H. Poincaré, Nonlinear Analysis 5 (1988), 179–207.

1987

• F. Dubois and P.G. LeFloch, Boundary condition for a system of conservation laws, C.R. Acad. Sc. Paris, Serie 1, 304 (1987), 75–78.
• A. Bourgeade, P.G. LeFloch, and P.-A. Raviart, Approximate solution of the generalized Riemann problem, Inter. Conf. on Hyperbolic Problems, Saint-Etienne (France), January 1986, Lect. Notes in Math., Vol. 1270, Springer Verlag, 1987, pp. 1–9.
• P.G. LeFloch and P.-A. Raviart, An asymptotic expansion for the solution of the generalized Riemann problem, C.R. Acad. Sc. Paris, Série 1, 304 (1987), 119–122.

1985

• P.G. LeFloch and J.-C. Nédélec, Weighted conservation laws, C.R. Acad. Sc. Paris, Série 1, 301 (1985), 793–796.

List by theme

Models from Continuum Physics and Mathematical Physics

Reviews and monographs

• P.G. LeFloch and M.-D. Thanh, The Riemann Problem in Continuum Physics, Applied Mathematical Sciences, Book Series Springer Verlag, 2024 (about 300 pages).
• P.G. LeFloch, Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues,, Lectures given at Centre for Advanced Study of the Norwegian Academy of Science and Letters, Oslo, Norway, Contemporary Mathematics, vol. 526, Amer. Math. Soc., Providence, RI, 2010, pp. 237–272. Also available at ArXiv: https://arxiv.org/abs/1002.2950.
• R.M. Colombo, Hyperbolic aspects of phase transition dynamics, D. Kröner and P.G. LeFloch, Abstracts from the mini-workshop held February 24–March 1, 2008, Oberwolfach Rep. 5 (2008), 513–556.
• P.G. LeFloch, An introduction to nonclassical shocks of systems of conservation laws, International School on Hyperbolic Problems, Freiburg, Germany, Oct. 97, D. Kröner, Russo M. Ohlberger and C. Rohde eds., Lect. Notes Comput. Eng., Vol. 5, Springer Verlag, 1999, pp. 28–72.

 

Fluid models, interfaces in materials, and rod linkage

• B. Boutin, F. Coquel, and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure, Networks Heter. Media 16 (2021), 283–315. [HAL]. Also available at HAL: https://hal.archives-ouvertes.fr/hal-02962629. Journal (DOI)
• Q. Du, Z. Huang, and P.G. LeFloch, Nonlocal conservation laws. A new class of monotonicity-preserving models, SIAM J. Numer. Anal. 55 (2017), 2465–2489. Journal (DOI)
• B. Boutin, F. Coquel, and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. IV. Well-balanced schemes for scalar multidimensional and multi-component laws, Math. Comp. 84 (2015), 1663–1702.
• B. Boutin, F. Coquel, and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. III. The well–balanced approximation of thick interfaces, SIAM J. Numer. Anal. 51 (2013), 1108–1133.
• B. Boutin, F. Coquel, and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. I. Self-similar diffusion for thin interfaces, Proc. Royal Soc. Edinburgh 141A (2011), 921–956.
• P.G. LeFloch and S. Mishra, Kinetic functions in magnetohydrodynamics with resistivity and Hall effects, Acta Math. Scientia 29B (2009), 1684–1702.
• A. Ambroso, B. Boutin, F. Coquel, E. Godlewski, and P.G. LeFloch, Coupling two scalar conservation laws via Dafermos self-similar regularization, Proc. ENUMATH 2007, 7th European Conf. on Numer. Math. Adv. Appl., Springer Verlag, Heidelberg, 2008, pp. 209–216.
• P.G. LeFloch, Propagating phase boundaries. Formulation of the problem and existence via the Glimm scheme, Arch. Rational Mech. Anal. 123 (1993), 153–197. Also available at ArXiv: https://arxiv.org/abs/math/0701646.
• P.G. LeFloch and F. Olsson, A second-order Godunov method for the conservation laws of nonlinear elastodynamics, Impact Comp. Sc. Eng. 2 (1990), 318–354.

 

Geometric flows, strings, and membranes

• S. Dong, P.G. LeFloch, and Z. Wyatt, Global evolution of the U(1) Higgs Boson: nonlinear stability and uniform energy bounds, Annals Henri Poincaré 22 (2021), 677–713. Also available at ArXiv: https://arxiv.org/abs/1902.02685.
• P.G. LeFloch, and W. Yan, Nonlinear stability of blow-up solutions to the Hyperbolic Mean Curvature flow, J. Differential Equations 269 (2020), 8269–8307. Journal (DOI)
• P.G. LeFloch and C.-H. Wei, ., Boundedness of the total energy of relativistic membranes evolving in a curved spacetime, J. Differential Equations 265 (2018), 312–331. Journal (DOI)
• N. Grubic, P.G. LeFloch, and C. Mardare, The equations of elastostatics in a Riemannian manifold, J. Math. Pures Appl. 102 (2014), 1121–1163.
• P.G. LeFloch and K. Smoczyk, The hyperbolic mean curvature flow, J. Math. Pures Appl. 90 (2008), 591–614. Also available at ArXiv: https://arxiv.org/abs/0712.0091.

 

Einstein gravity models and generalizations

• B. Le Floch and P.G. LeFloch, Optimal localization for the Einstein constraints, ArXiv:2312.17706, 2023. Also available at ArXiv: https://arxiv.org/abs/2312.17706.
• B. Le Floch and P.G. LeFloch, Optimal shielding for Einstein gravity, Class. Quantum Grav. 41 13LT02. Also available as ArXiv:2402.17598. Journal (DOI)
• P.G. LeFloch and F.C. Mena, A first-order formulation of f(R) gravity in spherical symmetry. Also available at ArXiv: https://arxiv.org/abs/2512.06908.
• P.G. LeFloch, F. Mena, and T.-C. Nguyen, Spherically symmetric evolution of self-gravitating massive fields, J. Differential Equ. 394 (2024) 31–97. Journal (DOI)
• P.G. LeFloch and T.-C. Nguyen, The seed-to-solution method for the Einstein constraints and the asymptotic localization problem, Jour. Funct. Anal. 285 (2023), 110106. Also available as ArXiv:1903.00243.. Journal (DOI)
• J.P. Dias and and P.G. LeFloch, A new approach to the Cauchy and Goursat problems for the nonlinear Wheeler-DeWitt equation, NoDEA (Nonlin. Differ. Equa. Appl.) 25 (2018), no. 2, Art. 10. Journal (DOI)
• P.G. LeFloch and Y. Ma, The mathematical validity of the f(R)-theory of modified gravity, Mém. Soc. Math. Fr. (N.S.) No. 150 (2017), 119 pp. Also available at ArXiv: https://arxiv.org/abs/1412.8151. Journal (DOI)
• D. Lee and P.G. LeFloch, The positive mass theorem for manifolds with distributional curvature, Comm. Math. Phys. 339 (2015), 99–120. Also available at ArXiv: https://arxiv.org/abs/1408.4431. Journal (DOI)
• P.G. LeFloch and C. Sormani, The nonlinear stability of rotationally symmetric spaces with low regularity, J. Funct. Anal. 268 (2015), 2005–2065. Also available at ArXiv: https://arxiv.org/abs/1401.6192. Journal (DOI)
• N. Bedjaoui, P.G. LeFloch, J. Martin-Garcia, and J. Novak, Existence of naked singularities for the Brans-Dicke theory. An analytical and numerical study, Class. Quantum Grav. 27 (2010), 245010. Also available at ArXiv: https://arxiv.org/abs/1008.4238.

 

Lorentzian geometry and spacetime foliations

• J.D.E. Grant and P.G. LeFloch, Null injectivity estimate under an upper bound on the curvature, Comm. Anal. Geom. 22 (2014), 965–996. Also available at ArXiv: https://arxiv.org/abs/1008.5167.
• P.G. LeFloch, Einstein spacetimes with weak regularity, in “Advances in Lorentzian Geometry”, Ed. M. Plaue, A.D. Rendall, and M. Scherfner, AMS/IP series, Vol. 49, 2011, pp. 81–96. Also available at ArXiv: https://arxiv.org/abs/1009.1884.
• P.G. LeFloch, Existence of CMC–harmonic coordinates for spacetimes with bounded curvature, Sémin. Théor. Spectr. Géom. (2011), Grenoble.
• P.G. LeFloch, C. Mardare, and S. Mardare, Isometric immersions into the Minkow\-ski spacetime for Lorentzian manifolds with limited regularity, Disc. Cont. Dyn. Syst. 23 (2009), 341–365. Also available at ArXiv: https://arxiv.org/abs/0712.4214.
• B.-L. Chen and P.G. LeFloch, Local foliations and optimal regularity of Einstein spacetimes, J. Geom. Phys. 59 (2009), 913–941. Also available at ArXiv: https://arxiv.org/abs/0812.5053. Journal (DOI)
• P.G. LeFloch, Local canonical foliations of Lorentzian manifolds with bounded curvature, in “Geometry, Topology, Quantum Fields Theories, and Cosmology”, J. Kouneiher, C. Barbachoux & F. Hélein eds., Edition Hermann Sciences, 2009. Also available at ArXiv: https://arxiv.org/abs/0812.3960.
• P.G. LeFloch, Injectivity radius and optimal regularity for Lorentzian manifolds with bounded curvature, Sémin. Théor. Spectr. Géom. 26 (2009), 77–90. Also available at ArXiv: https://arxiv.org/abs/0812.2671.
• B.-L. Chen and P.G. LeFloch, Injectivity radius estimates for Lorentzian manifolds, Commun. Math. Phys. 278 (2008), 679–713. Also available at ArXiv: https://arxiv.org/abs/math/0612860. Journal (DOI)

 

Self-gravitating compressible fluids and the Einstein equations

• B. Le Floch and P.G. LeFloch, Scattering laws for interfaces in self-gravitating matter flows, in preparation, 2026.
• B. Le Floch and P.G. LeFloch, Compensated compactness and corrector stress tensor for the Einstein equations in T2 symmetry, Portugaliae Math. 77 (2020), 409–421. See also ArXiv:1912.12981. Also available at ArXiv: https://arxiv.org/abs/1912.12981. Journal (DOI)
• B. Le Floch and P.G. LeFloch, On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry, Arch. Rational Mech. Anal. 233 (2019), 45–86. Also available at ArXiv: https://arxiv.org/abs/1805.10278. Journal (DOI)
• N. Grubic and P.G. LeFloch, On the area of the symmetry orbits in weakly regular Einstein-Euler spacetimes with Gowdy symmetry, SIAM J. Math. Anal. 47 (2015), 669–683. Also available at ArXiv: https://arxiv.org/abs/1411.3269.
• A. Burtscher and P.G. LeFloch, The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation, J. Math. Pures Appl. 102 (2014), 1164–1217. Also available at ArXiv: https://arxiv.org/abs/1411.3008. Journal (DOI)
• N. Grubic and P.G. LeFloch, Weakly regular Einstein–Euler spacetimes with Gowdy symmetry. The global areal foliation, Arch. Rational Mech. Anal. 208 (2013), 391–428. Also available at ArXiv: https://arxiv.org/abs/1212.1301.
• P.G. LeFloch and B.S. Tchapnda, Plane-symmetric spacetimes with positive cosmological constant. The case of stiff fluids, Adv. Theor. Math. Phys. 15 (2011), 1–26. Also available at ArXiv: https://arxiv.org/abs/1011.4571.
• P.G. LeFloch and A.D. Rendall, A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3, Arch. Rational Mech. Anal. 201 (2011), 841–870. Also available at ArXiv: https://arxiv.org/abs/1004.0427. Journal (DOI)
• P.G. LeFloch, Einstein-Euler equations for matter spacetimes with Gowdy symmetry, Séminaire X-EDP, Ecole Polytechnique, Palaiseau, 2009.
• P.G. LeFloch and J.M. Stewart, Shock waves and gravitational waves in matter spacetimes with Gowdy symmetry, Portugal. Math. 62 (2005), 349–370.

 

Perfect fluid flows in three space dimensions

• P.G. LeFloch and C.W. Wei, The global nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FRW geometry, Annals H. Poincaré, Nonlinear Analysis 38 (2021), 787–814. Also available at ArXiv: https://arxiv.org/abs/1512.03754.
• J. Jang, P.G. LeFloch, and N. Masmoudi, Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum, J. Differential Equa. 260 (2016), 5481–5509. Journal (DOI)
• R. Beig and P.G. LeFloch, Generalized relativistic hydrodynamics with a convex extension, Class. Quantum Grav. 31 (2014), 125005. Also available at ArXiv: https://arxiv.org/abs/1404.6403. Journal (DOI)
• P.G. LeFloch, Hyperbolic balance laws with entropy on a curved spacetime. The weak-strong uniqueness theory, J. Hyperbolic Differ. Equ. 10 (2013), 773–798.
• P.G. LeFloch and S. Ukai, A symmetrization of the relativistic Euler equations in several spatial variables, Kinetic & Related Models 2 (2009), 275–292. Also available at ArXiv: https://arxiv.org/abs/0812.4001.

 

Perfect fluid flows with symmetry

• P. Germain and P.G. LeFloch, The finite energy method for compressible fluids: the Navier-Stokes-Korteweg model, Comm. Pure Appl. Math. 64 (2016), 3–61.
• S. Georgiev and P.G. LeFloch, Generalized time-periodic solutions to the Euler equations of compressible fluids, Different. Equa. Appl. (DEA) 1 (2009), 413–426.
• P.G. LeFloch and M. Yamazaki, The dynamics of isothermal relativistic fluids, in Proc. of the RIMS Workshop on “Hyperfunctions and Linear Partial Differential Equations”, Kyoto, June 2006, Research Institute for Mathematical Sciences (RIMS), Sûrikaisekiken kyûsho Kôkyûroku No. 1648 (2009), 117–132.
• P.G. LeFloch and M. Yamazaki, Entropy solutions of the Euler equations for isothermal relativistic fluids, Intern. J. Dynamical Syst. Differential Equa. 1 (2007), 20–37. Also available at ArXiv: https://arxiv.org/abs/math/0701042.
• P.G. LeFloch and M. Westdickenberg, Finite energy solutions of the isentropic Euler equations, J. Math. Pures Appl. 88 (2007), 389–429. Also available at ArXiv: https://arxiv.org/abs/0812.2688.
• P.G. LeFloch and V. Shelukhin, Symmetries and global solvability of the isothermal gas dynamics equations, Arch. Rational Mech. Anal. 175 (2005), 389–430. Also available at ArXiv: https://arxiv.org/abs/math/0701100.
• P.G. LeFloch and V. Shelukhin, Symmetries and global solvability of the Cauchy problem for equations of the gas dynamics of isothermal flows, Doklady Math. Sc. 398 (2004), 300–305.
• G.-Q. Chen and P.G. LeFloch, Existence theory for the compressible isentropic Euler equations, Arch. Rational Mech. Anal. 166 (2003), 81–98.
• G.-Q. Chen and P.G. LeFloch, Compressible Euler equations with general pressure law, Arch. Rational Mech Anal. 153 (2000), 221–259.
• G.-Q. Chen and P.G. LeFloch, Entropies and weak solutions to the isentropic compressible Euler equations, C.R. Math. Acad. Sc. Paris 324 (1997), 1105–1110.
• F. Bereux, E. Bonnetier, and P.G. LeFloch, Gas dynamics equations. Two special cases, SIAM J. Math. Anal. 28 (1997), 499–515.
• P.G. LeFloch and Z.P. Xin, (unpublished)., Formation of singularities in periodic solutions to gas dynamics equations, \# 287, CMAP, Ecole Polytechnique (France), October 1993.
• P.G. LeFloch, Existence of entropy solutions for the compressible Euler equations, Conf. on “Hyperbolic Problems: theory, numerics, and applications” (Zürich, 1998), International Series Numer. Math. Vol. 130, Birkäuser Verlag Bäsel, Switzerland, 1999, pp. 599–607.

 

The Burgers model and its generalizations

• P.G. LeFloch and S. Xiang, Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime. II, J. Math. Pure Appl. 122 (2019), 272–317. Journal (DOI)
• P.G. LeFloch and S. Xiang, A numerical study of the relativistic Burgers and Euler equations on a Schwarzschild black hole exterior, Commun. Appl. Math. Comput. Sci. (CAMCOS) 13 (2018), 271–301.
• T. Ceylan, P.G. LeFloch, and B. Okutmustur, A finite volume method for the relativistic Burgers equation on a FLRW background spacetime, Commun. Comput. Phys. 23 (2018), 500–519.
• P.G. LeFloch and S. Xiang, Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime, J. Math. Pures Appl. 106 (2016), 1038–1090. Also available at ArXiv: https://arxiv.org/abs/1512.08253. Journal (DOI)
• P. Amorim, J.-P. Dias, M. Figueira, and P.G. LeFloch, The linear stability of shock waves for the nonlinear Schrödinger–inviscid Burgers system, J. Dyn. Diff. Equat. 25 (2013), 49–69.
• P.G. LeFloch, H. Makhlof, and B. Okutmustur, Relativistic Burgers equations on curved spacetimes. Derivation and finite volume approximation, SIAM J. Numer. Anal. 50 (2012), 2136–2158. Also available at ArXiv: https://arxiv.org/abs/1206.3018.
• P.G. LeFloch, Hyperbolic conservation laws on spacetimes, in “Nonlinear conservation laws and applications”, IMA Vol. Math. Appl. 153, Springer, New York, 2011, pp. 379–391. Also available at ArXiv: https://arxiv.org/abs/1006.2439.
• M. Ben-Artzi and P.G. LeFloch, The well-posedness theory for geometry compatible hyperbolic conservation laws on manifolds, Ann. Inst. Henri Poincaré — Nonlinear Analysis 24 (2007), 989—1008. Also available at ArXiv: https://arxiv.org/abs/math/0612846.

 

Mathematical Analysis of Partial Differential Equations

Reviews and monographs

• P.G. LeFloch and Y. Ma, The hyperboloidal foliation method for nonlinear wave equations,, World Scientific Press, Singapore, 2014 (150 pages). Also available at ArXiv: https://arxiv.org/abs/1411.4910.
• P.G. LeFloch, Hyperbolic Systems of Conservation Laws. The theory of classical and nonclassical shock waves, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2002 (300 pages).
• P.G. LeFloch, (unpublished)., On some nonlinear hyperbolic problems, Memoir of “Habilitation à Diriger des Recherches”, Université Pierre et Marie Curie (Paris 6), July 1990.
• P.G. LeFloch, (unpublished)., Theory and numerical approximation of nonlinear hyperbolic systems, Ph.D. Memoir in Applied Mathematics, Ecole Polytechnique, Palaiseau, France, January 1988..

 

The Euclidian-Hyperboloidal method and the stability of Minkowski space

• P.G. LeFloch and Y. Ma, and W. Zhang, The global nonlinear stability of Minkowski spacetime with self-gravitating massive Dirac fields, Monograph, October 2025. Also available at ArXiv: https://arxiv.org/abs/2510.20626 and HAL: https://hal.science/hal-05342436.
• P.G. LeFloch and Y. Ma, Nonlinear stability of self-gravitating massive fields, Annals of PDE 10 (2024), 16. Also available at ArXiv: https://arxiv.org/abs/1712.10045.
• P.G. LeFloch and Y. Ma, The Euclidean-hyperboloidal foliation method. Application to f(R) modified gravity, General Relativity and Gravitation 56 (2024), 66. Also available at ArXiv: https://arxiv.org/abs/2312.17712.
• S. Dong, P.G. LeFloch, and Z. Lei, The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded, Fundamental Research 4 (2024), 270–283. Also available at ArXiv: https://arxiv.org/abs/2103.07867. Journal (DOI)
• P.G. LeFloch, J. Oliver, and Y. Tsutsumi, Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model, J. Evol. Equ. 23 (2023), 75. Journal (DOI)
• P.G. LeFloch and Y. Ma, Nonlinear stability of self-gravitating massive fields. A wave-Klein-Gordon model, Class. Quantum Grav. 40 (2023), 154001. Also available at ArXiv: https://arxiv.org/abs/2212.07463. Journal (DOI)
• P.G. LeFloch and Y. Ma, Einstein-Klein-Gordon spacetimes in the harmonic near-Minkowski regime, Port. Math. 79 (2022), 343–393. Also available at ArXiv: https://arxiv.org/abs/2208.08676. Journal (DOI)
• P.G. LeFloch and Y. Ma, unpublished manuscript,, The Euclidean-hyperboidal foliation method and the nonlinear stability of Minkowski spacetime, ArXiv:1712.10048. Also available at ArXiv: https://arxiv.org/abs/1712.10048.
• P.G. LeFloch, , The global nonlinear stability of Minkowski spacetime for self-gravitating massive fields, Springer Nature 2018, C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems II, Springer Proc. in Mathematics & Statistics, Vol. 237. Also available at ArXiv: https://arxiv.org/abs/1612.09421.
• P.G. LeFloch and Y. Ma, The global nonlinear stability of Minkowski space for self-gravitating massive fields, World Scientific Press, Singapore, August 2017 (188 pages).
• P.G. LeFloch and Y. Ma, The global nonlinear stability of Minkowski space for self-gravitating massive fields. The wave-Klein-Gordon model, Comm. Math. Phys. 346 (2016), 603–665. Also available at ArXiv: https://arxiv.org/abs/1507.01143. Journal (DOI)
• P.G. LeFloch and Y. Ma, The global nonlinear stability of Minkowski spacetime for the Einstein equations in presence of massive fields, Note C.R. Acad. Sc. Paris 354 (2016), 948–953. Also available at ArXiv: https://arxiv.org/abs/1507.02715. Journal (DOI)
• A. Burtscher, J.D.E. Grant, and P.G. LeFloch, New energy inequalities for tensorial wave equations on spacetimes that satisfy a one-sided bound, Comm. Partial Diff. Equations 37 (2012), 1596–1619.

 

Fuchsian methods and the Big Bang singularity

• F. Beyer and P.G. LeFloch, Dynamics of self–gravitating fluids in Gowdy-symmetric spacetimes near cosmological singularities, Comm. Part. Diff. Equa. 42 (2017), 1199–1248. Also available at ArXiv: https://arxiv.org/abs/1512.07187.
• E. Ames, F. Beyer, J. Isenberg, and P.G. LeFloch, A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges, J. Geom. Phys. 121 (2017), 42–71. Also available at ArXiv: https://arxiv.org/abs/1602.03018. Journal (DOI)
• E. Ames, F. Beyer, J. Isenberg, and P.G. LeFloch, Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes, Ann. H. Poincaré 14 (2013), 1445–1523. Also available at ArXiv: https://arxiv.org/abs/1205.1881. Journal (DOI)
• E. Ames, Complex Analysis and Dynamical Systems V, F. Beyer, J. Isenberg, and P.G. LeFloch, Quasilinear symmetric hyperbolic Fuchsian systems in several space dimensions, Contemp. Math. 591 (2013), 1–19. Also available at ArXiv: https://arxiv.org/abs/1205.2166.
• F. Beyer and P.G. LeFloch, Second–order hyperbolic Fuchsian systems and applications, Class. Quantum Grav. 27 (2010), 245012–245033. Also available at ArXiv: https://arxiv.org/abs/1011.0270.
• F. Beyer and P.G. LeFloch, (unpublished)., Second-order hyperbolic Fuchsian systems. II. Gowdy spacetimes and the Fuchsian numerical algorithm, ArXiv:1006.2525. Also available at ArXiv: https://arxiv.org/abs/1006.2525.
• F. Beyer and P.G. LeFloch, (unpublished)., Second-order hyperbolic Fuchsian systems. I. General theory, ArXiv:1004.4885. Also available at ArXiv: https://arxiv.org/abs/1004.4885.
• P. Amorim and P.G. LeFloch, Sharp estimates for periodic solutions to the Euler–Poisson–Darboux equation, Portugal Math. 65 (2008), 387–429.

 

Methods for impulsive gravitational waves and cosmological singularities

• B. Le Floch, P.G. LeFloch, and G. Veneziano, Cyclic spacetimes through singularity scattering maps. Plane-symmetric gravitational collisions, Class. Quantum Grav. 39 (2022), 225010. Journal (DOI)
• B. Le Floch, P.G. LeFloch, and G. Veneziano, Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces, J. High Energy Phys. 04 (2022), 095. Journal (DOI)
• P.G. LeFloch, Gravitational singularities, scattering maps for bouncing, and structure-preserving algorithms, Proceedings of the Sixteenth Marcel Grossmann Meeting (MG16), Rome, Italy, 2021. Edited by G. Vereshchagin and R. Ruffini, World Scientific, 2022. See also ArXiv:2111.12650. Also available at ArXiv: https://arxiv.org/abs/2111.12650.
• P.G. LeFloch, Singularity scattering laws for bouncing cosmologies: a brief overview, Proceedings of the 10th International Meeting on Lorentzian Geometry, Springer Verlag, 2022. A. L. Albujer et al. (eds.), Developments in Lorentzian Geometry, Springer Proceedings in Mathematics & Statistics 389. See also ArXiv:2106.07958. Also available at ArXiv: https://arxiv.org/abs/2106.07958.
• B. Le Floch, P.G. LeFloch, and G. Veneziano, Universal scattering laws for quiescent bouncing cosmology, Physical Rev. D. 8 (2021), 083531. Journal (DOI)
• P.G. LeFloch and J. Smulevici, Future asymptotics and geodesic completeness of polarized T2-symmetric spacetimes, Annals and PDE 9 (2016), 363–395. Also available at ArXiv: https://arxiv.org/abs/1408.2084.
• P.G. LeFloch and J. Smulevici, Weakly regular T2-symmetric spacetimes. The future causal geometry of Gowdy spaces, J. Differ. Equa. 260 (2016), 1496–1521. Also available at ArXiv: https://arxiv.org/abs/1403.6252. Journal (DOI)
• P.G. LeFloch and J. Smulevici, Weakly regular T2 symmetric spacetimes. The global geometry of future Cauchy developments, J. Eur. Math. Soc. 17 (2015), 1229–1292. Also available at ArXiv: https://arxiv.org/abs/1012.5931.
• P.G. LeFloch and J.M. Stewart, The characteristic initial value problem for plane–symmetric spacetimes with weak regularity, Class. Quantum Grav. 28 (2011), 145019–145035. Also available at ArXiv: https://arxiv.org/abs/1004.2343.
• P.G. LeFloch and J. Smulevici, Global geometry of T2 symmetric spacetimes with weak regularity, Note C.R. Acad. Sc. 348 (2010), 1231–1233. Also available at ArXiv: https://arxiv.org/abs/1006.2933. Journal (DOI)
• P.G. LeFloch and C. Mardare, Definition and weak stability of spacetimes with distributional curvature, Portugal Math. 64 (2007), 535–573. Also available at ArXiv: https://arxiv.org/abs/0712.0122.

 

The theory of weak solutions to nonlinear hyperbolic systems

• P.G. LeFloch, Stability in the L1 norm via a linearization method for nonlinear hyperbolic systems, Proceedings of Hyp2008, 12th International Conference on Hyperbolic Problems, University of Maryland, College Park, June 2008, 2009. Also available at ArXiv: https://arxiv.org/abs/0812.3999.
• L. Ambrosio, G. Crippa, and P.G. LeFloch, Leaf superposition property for integer rectifiable currents, Netw. Heterog. Media 3 (2008), 85–95.
• O. Glass and P.G. LeFloch, Nonlinear hyperbolic systems : Non-degenerate flux, inner speed variation, and graph solutions, Arch. Rational Mech. Anal. 185 (2007), 409–480. Also available at ArXiv: https://arxiv.org/abs/math/0701041.
• J. Hong and P.G. LeFloch, A version of the Glimm method based on generalized Riemann problems, Portugal Math. 64 (2007), 199–236. Also available at ArXiv: https://arxiv.org/abs/math/0701063.
• P.G. LeFloch, Haar method, averaged matrix, wave cancellation, and L1 stability for hyperbolic systems, J. Hyperbolic Differ. Equ. 3 (2006), 701–739. Also available at ArXiv: https://arxiv.org/abs/0812.2685.
• P.G. LeFloch and H. Frid, Uniqueness for multidimensional hyperbolic systems with commuting Jacobians, Arch. Rational Mech. Anal. 182 (2006), 25–47.
• P.G. LeFloch, Graph solutions of nonlinear hyperbolic systems, J. Hyperbolic Differ. Equ. 1 (2004), 643–689.
• P.G. LeFloch and K. Trivisa, Continuous Glimm-type functionals and spreading of rarefaction waves, Comm. Math. Sci. 2 (2004), 213–236.
• T. Iguchi and P.G. LeFloch, Existence theory for hyperbolic systems of conservation laws with general flux-functions, Arch. Rational Mech. Anal. 168 (2003), 165–244.
• P. Goatin and P.G. LeFloch, L1 continuous dependence of entropy solutions for the compressible Euler equations, Comm. Pure Appl. Anal. 2 (2003), 107–137.
• J.-P. Dias and P.G. LeFloch, Some existence results on conservation laws with source-term, Math. Meth. Appl. Sc. 25 (2002), 1149–1160.
• P. Goatin and P.G. LeFloch, Sharp L1 continuous dependence of solutions of bounded variation for hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 157 (2001), 35–73.
• P. Goatin and P.G. LeFloch, Sharp L1 stability estimates for hyperbolic conservation laws, Portugal Math. 58 (2001), 1–44. Also available at ArXiv: https://arxiv.org/abs/math/0006109.
• J. Hu and P.G. LeFloch, L1 continuous dependence property for systems of conservation laws, Arch. Rational Mech. Anal. 151 (2000), 45–93.
• A. Bressan and P.G. LeFloch, Structural stability and regularity of entropy solutions to systems of conservation laws, Indiana Univ. Math. J. 48 (1999), 43–84.
• A. Bressan and P.G. LeFloch, Uniqueness of weak solutions to system of conservation laws, Arch. Rational Mech. Anal. 140 (1997), 301–331.
• B.T. Hayes and P.G. LeFloch, Measure-solutions to a strictly hyperbolic system of conservation laws, Nonlinearity 9 (1996), 1547–1563.
• P.G. LeFloch and Z.-P. Xin, Uniqueness via the adjoint problems for systems of conservation laws, Comm. Pure Appl. Math. 46 (1993), 1499–1533.

 

The DLM theory for nonconservative hyperbolic systems

• G. Crasta and P.G. LeFloch, A class of nonconservative and non strictly hyperbolic systems, Comm. Pure Appl. Anal. 1 (2002), 513–530.
• P.G. LeFloch and A. Tzavaras, Representation of weak limits and definition of nonconservative products, SIAM J. Math. Anal. 30 (1999), 1309–1342.
• P.G. LeFloch and A. Tzavaras, Existence theory for the Riemann problem for non-conservative hyperbolic systems, C.R. Acad. Sc. Paris, Série 1, 323 (1996), 347–352.
• G. Dal Maso, P.G. LeFloch, and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl. 74 (1995), 483–548.
• P.G. LeFloch and T.-P. Liu, Existence theory for nonlinear hyperbolic systems in nonconservative form, Forum Math. 5 (1993), 261–280.
• A. Forestier and P.G. LeFloch, Multivalued solutions to some nonlinear and nonstrictly hyperbolic systems, Japan J. Indus. Appl. Math. 9 (1992), 1–23.
• P.G. LeFloch, An existence and uniqueness result for two nonstrictly hyperbolic systems, IMA Volumes in Math. and its Appl.,“Nonlinear evolution equations that change type”, ed. B.L. Keyfitz and M. Shearer, Springer Verlag, Vol. 27, 1990, pp. 126–138.
• P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems in conservative form, Proc. Intern. Conf. on Hyperbolic problems, ed. J. Ballmann and R. Jeltsch, Notes on Num. Fluid Mech., Vol. 24, Viewieg, Braunschweig, 1989, pp. 362–373.
• P.G. LeFloch, (unpublished)., Shock waves for nonlinear hyperbolic systems in nonconservative form, Institute for Math. and its Appl., Minneapolis, IMA, \# 593, 1989 Available at:.
• P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems in nonconservative form, Comm. Part. Diff. Equa. 13 (1988), 669–727.
• P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems in nonconservative form, C.R. Acad. Sc. Paris, Série 1, 306 (1988), 181–186.

 

The theory of boundary conditions for hyperbolic systems

• A.P. Choudhury, K.T. Joseph, and P.G. LeFloch, The mathematical theory of self–similar boundary layers for nonlinear hyperbolic systems with viscosity and capillarity, Bull. Inst. Math. Acad. Sinica 10 (2015), 639–693.
• K.T. Joseph and P.G. LeFloch, Singular limits for the Riemann problem: general diffusion, relaxation, and boundary conditions, C.R. Math. Acad. Sci. Paris 344 (2007), 59–64. Also available at ArXiv: https://arxiv.org/abs/0812.2680.
• K.T. Joseph and P.G. LeFloch, Singular limits for the Riemann problem. General diffusion, relaxation, and boundary conditions, in “New analytical approach to multidimensional balance laws”, O. Rozanova ed., Nova Press, 2006, pp. 143–172.
• K.T. Joseph and P.G. LeFloch, Boundary layers in weak solutions of hyperbolic conservation laws. III. Vanishing relaxation limits, Portugal. Math. 59 (2002), 453.
• K.T. Joseph and P.G. LeFloch, Boundary layers in weak solutions of hyperbolic conservation laws. II. Self-similar vanishing diffusion limits, Comm. Pure Appl. Anal. 1 (2002), 51–76.
• C. Kondo and P.G. LeFloch, Measure-valued solutions and well-posedness of multi-dimen\-sional conservation laws in a bounded domain, Portugal Math. 58 (2001), 171–194.
• K.T. Joseph and P.G. LeFloch, Boundary layers in weak solutions to hyperbolic conservation laws, Arch. Rational Mech Anal. 147 (1999), 47–88. (First appeared as: \# 341, CMAP, Ecole Polytechnique (France), November 1996.). Also available at ArXiv: https://arxiv.org/abs/math/0702024.
• F. Dubois and P.G. LeFloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, Proc. Inter. Conf. on Hyperbolic problems, Aachen (Germany), March 1988, Notes on Numer. Fluid Mech., Vol. 24, Vieweg, 1989, pp. 96-106.
• F. Dubois and P.G. LeFloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations 71 (1988), 93–122.
• F. Dubois and P.G. LeFloch, Boundary condition for a system of conservation laws, C.R. Acad. Sc. Paris, Serie 1, 304 (1987), 75–78.

 

The mathematical theory of kinetic relations

• E. Kardhashi, M. Laforest, and P.G. LeFloch, The mathematical theory of splitting-merging patterns in phase transition dynamics, Comm. Partial Differential Equations 47 (2022), 1339–1393. Also available at ArXiv: https://arxiv.org/abs/2105.06664. Journal (DOI)
• C. Berthon, F. Coquel, and P.G. LeFloch, Why many theories of shock waves are necessary. Kinetic relations for nonconservative systems, Proc. Royal Soc. Edinburgh 137 (2012), 1–37.
• M. Laforest and P.G. LeFloch, Diminishing functionals for nonclassical entropy solutions selected by kinetic relations, Portugal Math. 67 (2010), 279–319. Also available at ArXiv: https://arxiv.org/abs/0812.4021.
• P.G. LeFloch, Existence and qualitative properties of kinetic functions generated by diffusive-dispersive regularizations, Contemp. Mat. 37 (2009), 43–89. Also available at ArXiv: https://arxiv.org/abs/1005.2479.
• N. Bedjaoui, C. Chalons, F. Coquel, and P.G. LeFloch, Non-monotonic traveling waves in Van der Waals fluids, Analysis Appl. 3 (2005), 419–446.
• N. Bedjaoui, C. Klingenberg, and P.G. LeFloch, On the validity of the Chapman-Enskog expansion for shock waves with small strength, Portugal. Math. 61 (2004). 479–499. Also available at ArXiv: https://arxiv.org/abs/0812.3985.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. V. Singular diffusion and dispersion terms, Proc. Royal Soc. Edinburgh 134A (2004), 815–844.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. IV. Compressible Euler system, Chinese Ann. Appl. Math. 24 (2003), 17–34.
• P.G. LeFloch and M. Shearer, Nonclassical Riemann solvers with nucleation, Proc. Royal Soc. Edinburgh 134A (2004), 941–964.
• P. Baiti, P.G. LeFloch, and B. Piccoli, Existence theory for nonclassical entropy solutions: scalar conservation laws, Z. Angew. Math. Phys. 55 (2004), 927–945.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. II. An hyperbolic-elliptic model of phase transitions, Proc. Royal Soc. Edinburgh 132 (2002), 545–565.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. I. Nonconvex hyperbolic conservation laws, J. Differential Equations 178 (2002), 574–607.
• P. Baiti, P.G. LeFloch, and B. Piccoli, Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems, J. Differential Equations 172 (2001), 59–82.
• N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. III. An hyperbolic model of nonlinear elastodynamics, Ann. Univ. Ferrara Sc. Mat. 47 (2001), 117–144.
• P. Baiti, P.G. LeFloch, and B. Piccoli, BV Stability via generalized characteristics for nonclassical solutions of conservation laws, EQUADIFF’99, Proc. Internat. Conf. Differ. Equ., Berlin, August 1999, B. Fiedler, K. Gröger, and J.Sprekels, editors, World Sc. Publ., River Edge, NY, 2000, pp. 289–294.
• B.T. Hayes and P.G. LeFloch, Nonclassical shock waves and kinetic relations. Strictly hyperbolic systems, SIAM J. Math. Anal. 31 (2000), 941–991. (First appeared as : \# 357, CMAP, Ecole Polytechnique (France), November 1996.).
• P. Baiti, P.G. LeFloch, and B. Piccoli, Nonclassical shocks and the Cauchy problem. General conservation laws, Contemporary Math. 238 (1999), 1–25.
• D. Amadori, P. Baiti, P.G. LeFloch and B. Piccoli, Nonclassical shocks and the Cauchy problem for nonconvex conservation laws, J. Differential Equations 151 (1999), 345–372.
• B.T. Hayes and P.G. LeFloch, Nonclassical shocks and kinetic relations. Scalar conservation laws, Arch. Rational Mech. Anal. 139 (1997), 1–56.

 

The vanishing diffusive-dispersive limits

• F. Kissling, P.G. LeFloch, and C. Rohde, A kinetic decomposition for singular limits of non-local conservation laws, J. Differential Equations 247 (2009), 3338–3356.
• K.T. Joseph and P.G. LeFloch, Singular limits in phase dynamics with physical viscosity and capillarity, Proc. Royal Soc. Edinburgh 137A (2007), 1287–1312. Also available at ArXiv: https://arxiv.org/abs/math/0701007.
• C. Kondo and P.G. LeFloch, Zero diffusion-dispersion limits for hyperbolic conservation laws, SIAM Math. Anal. 33 (2002), 1320–1329. Also available at ArXiv: https://arxiv.org/abs/0712.0094.
• P.G. LeFloch and C. Rohde, The zero diffusion-dispersion limit for the Riemann problem, Indiana Univ. Math. J. 50 (2001), 1707–1743.
• P.G. LeFloch and R. Natalini, Conservation laws with vanishing nonlinear diffusion and dispersion, Nonlinear Analysis 36 (1999), 213–230. Also available at ArXiv: https://arxiv.org/abs/0711.0411.
• J.M. Correia and P.G. LeFloch, Nonlinear hyperbolic conservation laws, in “Nonlinear evolution equations and their applications” (Macau, 1998), World Sci. Publ., River Edge, NJ, 1999, pp. 21–44.
• J.M. Correia and P.G. LeFloch, Nonlinear diffusive-dispersive limits for multidimensional conservation laws, in “Advances in Nonlinear P.D.E.’s and Related Areas”, (Beijing, 1997), World Sci. Publ., River Edge, NJ, 1998, pp. 103–123. Also available at ArXiv: https://arxiv.org/abs/0810.1880.

 

The Hopf-Lax-Oleinik formula and its generalizations

• Y. Bakhtin and P.G. LeFloch, Ergodicity of spherically symmetric fluid flows outside of a Schwarzschild black hole with random boundary forcing, Stoch PDE: Anal. Comp. 6 (2018), 746–785. Also available at ArXiv: https://arxiv.org/abs/1706.01004.
• P.G. LeFloch and S. Xiang, Existence and uniqueness results for the pressureless Euler-Poisson system, Portugal Math. 72 (2015), 229–246.
• P.G. LeFloch and J.-C. Nédélec, Asymptotic time-behavior for weighted scalar nonlinear conservation laws, RAIRO: Math. Model. Num. Anal. 22 (1988), 469–475.
• P.G. LeFloch and J.-C. Nédélec, Explicit formula for weighted scalar nonlinear conservation laws, Trans. Amer. Math. Soc. 308 (1988), 667–683.
• P.G. LeFloch, Explicit formula for scalar conservation laws with boundary condition, Math. Meth. Appl. Sc. 10 (1988), 265–287.
• P.G. LeFloch and J.-C. Nédélec, Weighted conservation laws, C.R. Acad. Sc. Paris, Série 1, 301 (1985), 793–796.

 

Structure-Preserving Approximation of Partial Differential Equations

Machine Learning

• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, A class of kernel-based scalable algorithms for data science Also available at ArXiv: https://arxiv.org/abs/2410.14323.
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, Extrapolation and generative algorithms for three applications in finance, The Willmot Journal, September 2024, pp. 54–60. Available at. Also available at ArXiv: https://arxiv.org/abs/2404.13355. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, Mesh-free algorithms for a class of problems arising in finance and machine learning, J. Sc. Comput. 95 (2023), 75. Also available at ArXiv: https://arxiv.org/abs/2304.10521. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, technical report, Predictive machines with uncertainty quantification, available at.
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, technical report, CodPy: a kernel-based ordering algorithm, available at.
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, technical report, CodPy: an advanced tutorial, available at.
• P.G. LeFloch, J.-M. Mercier, and S. Miryusupov, technical report, CodPy: a tutorial, available at.
• P.G. LeFloch and J.-M. Mercier, Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions, Comput. Methods Appl. Mech. Engrg. 369 (2020), 113245. Also available at ArXiv: https://arxiv.org/abs/1911.00795. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, The Transport-based Mesh-free Method (TMM). A short review, The Wilmott journal 109 (2020), 52–57. Also available at ArXiv:1911.00992 and. Journal (DOI)
• P.G. LeFloch and J.-M. Mercier, A new method for solving Kolmogorov equations in mathematical finance, C.R. Math. Acad. Sci. Paris 355 (2017), 680–686. Also available at ArXiv: https://arxiv.org/abs/1606.09612. Journal (DOI)
• P.G. LeFloch and J.M. Mercier, Revisiting the method of characteristics via a convex hull algorithm, J. Comput. Phys. 298 (2015), 95–112. Also available at ArXiv: https://arxiv.org/abs/1409.0291.

 

Entropy-preserving approximation

• P.G. LeFloch, J.-M. Mercier, and C. Rohde, Fully discrete entropy conservative schemes of arbitrary order, SIAM J. Numer. Anal. 40 (2002), 1968–1992.
• C. Chalons and P.G. LeFloch, High-order entropy conservative schemes and kinetic relations for van der Waals fluids, J. Comput. Phys. 167 (2001), 1–23.
• G.-Q. Chen and P.G. LeFloch, Entropies and entropy-flux splittings for the isentropic Euler equations, Chinese Annal. Math. 22 (2001), 1–14.
• P.G. LeFloch and C. Rohde, High-order schemes, entropy inequalities, and nonclassical shocks, SIAM J. Numer. Anal. 37 (2000), 2023–2060.
• P.G. LeFloch, An entropy diminishing criterion for hyperbolic conservation laws, in “Numerical methods for wave propagation” (Manchester, 1995), Fluid Mech. Appl. 47, Kluwer Acad. Publ., Dordrecht, 1998, pp. 275–295.
• G.-Q. Chen and P.G. LeFloch, Entropy flux splittings for hyperbolic conservation laws. General framework, Comm. Pure Appl. Math. 48 (1995), 691–729.
• F. Coquel and P.G. LeFloch, An entropy satisfying second order scheme for systems of conservation laws, C.R. Acad. Sc. Paris, Série 1, 320 (1995), 1263–1268.
• G.-Q. Chen and P.G. LeFloch, Entropy flux-splittings for hyperbolic conservation laws, C.R. Acad. Sc. Paris, Série 1, 317 (1993), 761–766.

 

Geometry-preserving approximation

• P.G. LeFloch, C. Parés, and E. Pimentel-García, A class of well-balanced algorithms for relativistic fluids on a Schwarzschild background, Journal of Scientific Computing 89 (2021), 1–43. See also ArXiv:2011.07587. Journal (DOI)
• J. Giesselman and P.G. LeFloch, Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary, Numerische Mathematik 144 (2020), 751–785. Journal (DOI)
• S. Dong and P.G. LeFloch, Convergence of the finite volume method on a Schwarzschild background, ESAIM-M2AN (2019), 1459–1476. Also available at ArXiv: https://arxiv.org/abs/1901.10973.
• A. Beljadid, P.G. LeFloch, and M. Mohamadian, Late-time asymptotic behavior of solutions to hyperbolic conservation laws on the sphere, Comput. Methods Appl. Mech. Engrg. 349 (2019), 285–311. Journal (DOI)
• A. Beljadid and P.G. LeFloch,, A central-upwind geometry-preserving method for hyperbolic conservation laws on the sphere, Commun. Appl. Math. Comput. Sci. 12 (2017), 81–107.
• P.G. LeFloch and H. Makhlof, A geometry-preserving finite volume method for compressible fluids on Schwarzschild spacetime, Commun. Comput. Phys. 15 (2014), 827–852. Also available at ArXiv: https://arxiv.org/abs/1212.6622. Journal (DOI)
• M. Ben-Artzi, J. Falcovitz, and P.G. LeFloch, Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme, J. Comput. Phys. 228 (2009), 5650–5668. Also available at ArXiv: https://arxiv.org/abs/0808.2062.
• P.G. LeFloch and B. Okutmustur, Hyperbolic conservation laws on manifolds with limited regularity, C.R. Math. Acad. Sc. Paris 346 (2008), 539–543. Also available at ArXiv: https://arxiv.org/abs/0808.2895.
• P.G. LeFloch and M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section, Comm. Math. Sci. 1 (2003), 763–796.

 

Small-scale preserving approximation

• P.G. LeFloch and and A.D. Tesdall, The positive entropy production property for augmented nonlinear hyperbolic models, Comptes Rendus Mathématiques 360 (2022), 35–46. Also available at ArXiv: https://arxiv.org/abs/1912.03563. Journal (DOI)
• P.G. LeFloch and H. Ranocha, Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts, Jour. Scientific Comput. 87 (2021), 1–38. Also available at ArXiv: https://arxiv.org/abs/2007.08780. Journal (DOI)
• A. Beljadid, P.G. LeFloch, S. Mishra, and C. Pares, Schemes with well-controlled dissipation. Hyperbolic systems in nonconservative form, Commun. in Comput. Phys. 21 (2017), 913–946.
• J. Ernest, P.G. LeFloch, and S. Mishra, Schemes with well-controlled dissipation (WCD), SIAM J. Numer. Anal. 53 (2015), 674–699.
• P.G. LeFloch and S. Mishra, Numerical methods with controled dissipation for small-scale dependent shocks, Acta Numer. 23 (2014), 743—-816. Also available at ArXiv: https://arxiv.org/abs/1312.1280.
• M.J. Castro, P.G. LeFloch, M.L. Munoz-Ruiz, and C. Pares, Numerical investigation of finite difference schemes for nonconservative hyperbolic systems, in “Hyperbolic problems: theory, numerics and applications”, Proc. Sympos. Appl. Math., 67, Part 2, Amer. Math. Soc., Providence, RI, 2009, pp. 465–475.
• M.J. Castro, P.G. LeFloch, M.L. Munoz-Ruiz, and C. Pares, Why many theories of shock waves are necessary. Convergence error in formally path-consistent schemes, J. Comput. Phys. 227 (2008), 8107–8129. Also available at ArXiv: https://arxiv.org/abs/0808.2065.
• P.G. LeFloch and M. Mohamadian, Why many shock wave theories are necessary. Fourth-order models, kinetic functions, and equivalent equations, J. Comput. Phys. 227 (2008), 4162–4189. Also available at ArXiv: https://arxiv.org/abs/0712.3810.
• C. Chalons and P.G. LeFloch, A fully discrete scheme for diffusive-dispersive conservation laws, Numerische Math. 89 (2001), 493–509.
• B.T. Hayes and P.G. LeFloch, Nonclassical shocks and kinetic relations. Finite difference schemes, SIAM J. Numer. Anal. 35 (1998), 2169–2194.
• T.Y. Hou and P.G. LeFloch, Why nonconservative schemes converge to wrong solutions. Error analysis, Math. of Comput. 62 (1994), 497–530.

 

Time-asymptotics preserving approximation

• Y.-Y. Cao, M.A. Ghazizadeh, and P.G. LeFloch, Asymptotic structure of cosmological fluid flows in one and two space dimensions: a numerical study, Commun. Appl. Math. Comput. Sci. 17 (2022), 79–129. Also available at ArXiv: https://arxiv.org/abs/1912.13439. Journal (DOI)
• H. Karjoun, A. Beljadid, and P.G. LeFloch, A structure-preserving algorithm for surface water flows with transport processes, Adv. Comput. Math. 48 (2022), 7. Also available at ArXiv: https://arxiv.org/abs/2012.13702. Journal (DOI)
• F. Beyer and P.G. LeFloch, A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes, J. Comput. Phys. 431 (2021), 110145. Also available at ArXiv: https://arxiv.org/abs/2005.13504. Journal (DOI)
• Y.-Y. Cao, M.A. Ghazizadeh, and P.G. LeFloch, Asymptotic structure of cosmological Burgers flows in one and two space dimensions: a numerical study, Communications in Computational Physics 29 (2021), 472–509. Also available at ArXiv: https://arxiv.org/abs/1911.07239. Journal (DOI)
• S. Boscarino, P.G. LeFloch, and G. Russo, High–order asymptotic preserving methods for fully nonlinear relaxation problems, SIAM J. Sci. Comput. 36 (2014), 377–395. Also available at ArXiv: https://arxiv.org/abs/1210.4761.
• P.G. LeFloch, Structure-preserving shock-capturing methods: late-time asymptotics, curved geometry, small-scale dissipation, and nonconservative products,, in “Lecture Notes of the XV Jacques-Louis Lions Spanish-French School”, Ed. C. Parès, C. Vázquez, and F. Coquel, Springer Verlag, Switzerland, 2014, pp. 179–222. Also available at ArXiv: https://arxiv.org/abs/1512.08181.
• P.G. LeFloch, A framework for late-time/stiff relaxation asymptotics, in “The Courant-Friedrichs-Lewy (CFL) condition”, Birkhäuser & Springer, New York, 2013, pp. 119–137.
• C. Berthon, P.G. LeFloch, and R. Turpault, Late-time/stiff-relaxation asymp\-totic-preserving approximations of hyperbolic equations, Math. of Comput. 82 (2013), 831–860.
• P.G. LeFloch and M.-D. Thanh, A Godunov-type method for the shallow water equations with variable topography in the resonant regime, J. Comput. Phys. 230 (2011), 7631–7660.
• F. Beyer and P.G. LeFloch, Second–order hyperbolic Fuchsian systems. Asymptotic behavior of geodesics in Gowdy spacetimes, Phys. Rev. D. 84 (2011), 084036. Also available at ArXiv: https://arxiv.org/abs/1108.4718.
• P. Amorim, C. Bernardi, and P.G. LeFloch, Computing Gowdy spacetimes via spectral evolution in future and past directions, Class. Quantum Grav. 26 (2009), 1–18. Also available at ArXiv: https://arxiv.org/abs/0811.1266. Journal (DOI)
• D. Kröner, P.G. LeFloch, and M.D. Thanh, The minimum entropy principle for fluid flows in a nozzle with discontinuous cross-section, Math. Meth. Appl. Sc. (M2AN) 42 (2008), 425–442.
• P.G. LeFloch and M.D. Thanh, The Riemann problem for the shallow water equations with discontinuous topography, Comm. Math. Sci. 5 (2007), 865–885. Also available at ArXiv: https://arxiv.org/abs/0712.3778.

 

Front-tracking and random-choice methods

• B. Boutin, C. Chalons, F. Lagoutière, and P.G. LeFloch, Convergent and conservative schemes for nonclassical solutions based on kinetic relations, Interfaces and Free Boundaries 10 (2008), 399–421.
• B. Boutin, C. Chalons, F. Lagoutière and P.G. LeFloch, A sharp interface and fully conservative scheme for computing nonclassical shocks, in “Numerical Mathematics and Advanced Applications”, Proc. ENUMATH 2007, 7th European Conf. on Numer. Math. Adv. Appl., Graz, Austria, September 2007, Springer Verlag, Heidelberg, K. Kunisch, G. Of, and O. Steinbach (Eds.), 2008, pp. 217–224.
• A.P. Barnes, P.G. LeFloch, B.G. Schmidt, and J.M. Stewart, The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes, Class. Quantum Grav. 21 (2004), 5043–5074.
• C. Chalons and P.G. LeFloch, Computing undercompressive waves with the random choice scheme. Nonclassical shock waves, Interfaces and Free Boundaries 5 (2003), 129–158.
• T.Y. Hou, P. Rosakis, and P.G. LeFloch, A level set approach to the computation of twinning and phase transition dynamics, J. Comput. Phys. 150 (1999), 302–331.
• P.G. LeFloch, Dynamics of solid-solid phase interfaces via a level set approach, Proc. Fifth Workshop on Partial Differential Equations (Rio de Janeiro, 1997), Mat. Contemp. 15 (1998), pp. 187–212.
• P.G. LeFloch, Computational Methods for propagating phase boundaries, in “Intergranular and Interphase Boundaries in Materials: iib95”, Lisbon, June 1995, Eds. A.C. Ferro, J.P. Conde and M.A. Fortes. Material Science Forum Vols. 207–209, 1996, pp. 509–515.
• X.-G. Zhong, T.Y. Hou, and P.G. LeFloch, Computational methods for propagating phase boundaries, J. Comput. Phys. 124 (1996), 192–216.

 

Explicit Riemann solvers

• P. Goatin and P.G. LeFloch, The Riemann problem for a class of resonant nonlinear systems of balance laws, Ann. Inst. H. Poincaré – Analyse Non-linéaire 21 (2004), 881–902.
• P.G. LeFloch and M.D. Thanh, Properties of Rankine-Hugoniot curves for Van der Waals fluids, Japan J. Indust. Applied Math. 20 (2003), 211–238.
• J.M. Correia, P.G. LeFloch, and M.D. Thanh, Hyperbolic conservation laws with Lipschitz continuous flux-functions. The Riemann problem, Bol. Soc. Bras. Mat. 32 (2001), 271–301.
• P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations I. A nonconvex hyperbolic model of phase transitions, Z. Angew. Math. Phys. 52 (2001), 597–619.
• P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase transitions, Proc. Royal Soc. Edinburgh 132A (2001), 181–219.
• P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations. III. A nonconvex hyperbolic model for Van der Waals fluids, Electr. J. Diff. Equa. 72 (2000), 1–19.
• P.G. LeFloch and T.-T. Li, A global in time asymptotic expansion for the solution of the generalized Riemann problem, Asymp. Analysis 3 (1991), 321-340.
• A. Bourgeade, P.G. LeFloch, and P.-A. Raviart, An asymptotic expansion for the solution of the generalized Riemann problem. Part II. Application to the gas dynamics equations, Ann. Inst. H. Poincaré, Nonlin. Anal. 6 (1989), 437-480.
• P.G. LeFloch and T.-T. Li, A global in time asymptotic expansion for the solution of the generalized Riemann problem, C.R. Acad. Sc. Paris, Série 1, 309 (1989), 807–810.
• P.G. LeFloch and P.-A. Raviart, An asymptotic expansion for the solution of the generalized Riemann problem. Part I. General theory, Ann. Inst. H. Poincaré, Nonlinear Analysis 5 (1988), 179–207.
• A. Bourgeade, P.G. LeFloch, and P.-A. Raviart, Approximate solution of the generalized Riemann problem, Inter. Conf. on Hyperbolic Problems, Saint-Etienne (France), January 1986, Lect. Notes in Math., Vol. 1270, Springer Verlag, 1987, pp. 1–9.
• P.G. LeFloch and P.-A. Raviart, An asymptotic expansion for the solution of the generalized Riemann problem, C.R. Acad. Sc. Paris, Série 1, 304 (1987), 119–122.

 

First-order accuracy in hyperbolic conservation laws

• P. Amorim, P.G. LeFloch, and W. Neves, A geometric approach to error estimates for conservation laws posed on a spacetime, Nonlinear Anal. TMA 74 (2011), 4898–4917. Also available at ArXiv: https://arxiv.org/abs/1002.3137.
• P.G. LeFloch, W. Neves, and B. Okutmustur, Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes, Acta Math. Sinica 25 (2009), 1041–1066.
• P. Amorim, P.G. LeFloch, and B. Okutmustur, Finite volume schemes on Lorentzian manifolds, Comm. Math. Sc. 6 (2008), 1059–1086.
• P.G. LeFloch and B. Okutmustur, Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms, Far East J. Math. Sci. 31 (2008), 49–83. Also available at ArXiv: https://arxiv.org/abs/0810.0255.
• P. Amorim, M. Ben-Artzi, and P.G. LeFloch, Hyperbolic conservation laws on manifolds: Total variation estimates and finite volume method, Meth. Appl. Analysis 12 (2005), 291–324. Also available at ArXiv: https://arxiv.org/abs/math/0612847.
• B. Cockburn, F. Coquel, and P.G. LeFloch, Convergence of finite volume methods for multidimensional conservation laws, SIAM J. Numer. Anal. 32 (1995), 687–705.
• B. Cockburn, F. Coquel, and P.G. LeFloch, Error estimates for finite volume methods for multidimensional conservation laws, Math. of Comput. 63 (1994), 77–103. (First appeared as: 91-20, AHCRC Institute, Minneapolis, USA, 1991.).

 

Second-order accuracy in hyperbolic conservation laws

• P.G. LeFloch and J.-G. Liu, Generalized monotone schemes, extremum paths and discrete entropy conditions, Math. of Comput. 68 (1999), 1025–1055. Also available at ArXiv: https://arxiv.org/abs/0711.0406.
• F. Coquel and P.G. LeFloch, An entropy satisfying MUSCL scheme for systems of conservation laws, Numer. Math. 74 (1996), 1–33.
• P.G. LeFloch, Monotonicity consistent scheme for hyperbolic conservation laws, Proc. “Fifth International Colloquium on Numerical Analysis”, Plovdiv, August 1995, ed. D. Bainov.
• P.G. LeFloch and J.-G. Liu, Discrete entropy and monotonicity criterion for hyperbolic conservation laws, C.R. Acad. Sc. Paris, Série I, 319 (1994), 881–886.
• F. Coquel and P.G. LeFloch, Convergence of finite difference schemes for scalar conservation laws in several space variables. General theory, SIAM J. Numer. Anal. 30 (1993), 675–700.
• F. Coquel and P.G. LeFloch, Convergence of finite difference schemes for scalar conservation laws in several space variables. The corrected antidiffusive-flux approach, Math. of Comput. 57 (1991), 169–210.
• F. Coquel and P.G. LeFloch, Convergence of finite difference schemes for conservation laws in several space dimensions, C.R. Acad. Sc. Paris, Série 1, 310 (1990), 455–460.