Publications

116. Long-time behavior, invariant measures and regularizing effects for stochastic scalar conservation laws (with B. Gess). arXiv:1411.3939. arXiv
115. Large time average of reachable sets and applications to the homogenization of interfaces moving with oscillatory velocity (with W. Jing and H. Tran). preprint, arXiv:1408.2013. arXiv
114. Quantitative homogenization of elliptic pde with random oscillatory boundary data (with W. Feldman and I. Kim), J. Math. Pure Appl., to appear. arXiv
113. Scalar conservation laws with multiple rough fluxes (with B. Gess), Comm. Math. Sci, to appear. arXiv
112. Stochastic homogenization of interfaces moving with changing sign normal velocity (with A. Ciomaga and H. Tran), J. Differential Equations 258 (2015), no. 4, 1025-1057. link
111. Metastability properties for parabolic equations with drift: Part 1 (with H. Ishii), Indiana Univ. Math. Journal, to appear. arXiv
110. Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case (with P.-L. Lions and B. Perthame). Stoch. Partial Diff. Equ. Anal. Comp. 2 (2014), no. 4, 517-538. link
109. Periodic approximations of the ergodic constants in the stochastic homogenization (with P. Cardaliaguet), Ann. Inst. H. Poincare Anal. Non Lineaire 32 (2015), no.1, 41-58. arXiv
108. Time fluctuations in a population model of adaptive dynamics (with S. Mirrahimi and B. Perthame), Ann. Inst. H. Poincare Anal. Non Lineaire, to appear. link
107. Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations (with S. Armstrong and P. Cardaliaguet), J. Amer. Math. Soc. 27 (2014), no. 2, 479--540. link
106. Concentration for neutronic multigroup diffusion in random environments (with S. Armstrong, Ann. I. H. Poincare Anal. Non Lineaire 30 (2013), no. 3., 419--439. link
105. Scalar conservation laws with rough (stochastic) fluxes (with B.~Perthame and P.-L.~Lions). Stoch. Partial Diff. Equ. Anal. Comp. 1 (2013), no. 4, 664--686. arXiv
104. Stochastic homogenization of level-set convex Hamilton-Jacobi equations (with S. Armstrong), Int. Math. Res. Not. 2013 (2013), no. 17, 3420--3449. arXiv
103. Stochastic averaging lemmas for kinetic equations (with P.-L. Lions and B. Perthame), Seminaire Equations Aux Derivee Partielles (Ecole Polytechnique) 2011-2012, no. 1.. arXiv
102. A homogenization approach for the motion of motor proteins (with S. Mirrahimi), NODEA Nonlinear Differential Equatiions Appl. 20 (2013), no. 1, 129--147. link
101. Homogenization and enhancement of the $G$-equation in random environments (with P. Cardaliaguet), Comm. Pure Appl. Math. 60 (2013), no. 10, 1582--1628. link
100. Homogenization of $L^\infty$ variational problems (with S. Armstrong), Adv. Math. 229 (2012), no. 6, 3508--3535.arXiv
99. A pde approach to small stochastic perturbations of Hamiltonian flows (with H. Ishii), J. Differential Equations 252, no. 2, 1748-1775. link
98. Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments (with S. Armstrong), J. Math. Pure Appl. (9) 97 (2012), no. 5, 460-504. link
97. Singular Hamilton-Jacobi equation for the tail problem (with S. Mirrahimi, G. Barles and B. Perthame), SIAM J. Math. Analysis 44 2012, no. 6, 4297-4319. link
96. Homogenization and enhancement for the G-equation in periodic media (with P. Cardaliaguet and J. Nolen), Arch. Ration. Mech. Anal. 199 (2011), no. 2, 527-561. link
95. A homogenization approach to flashing ratchets (with B. Perthame), Nonlinear Differential Equations Appl. 18 (2011), no. 1, 45-58. link
94. Rates of convergence for the homogenization of uniformly elliptic pde in random media (with L. Caffarelli), Invent. Math. 180 (2010), no. 2, 301-360. link
93. Existence and uniqueness of weak solutions for precipitating fronts: A novel hyperbolic free boundary problem in several space dimensions (with A. J. Majda), Comm. Pure Appl. Math. 63 (2010), no. 10, 1351-1361. link
92. Stochastic homogenization for Hamilton-Jacobi and "viscous" Hamilton-Jacobi equations with convex nonlinearities- revisited (with P.-L. Lions), Comm. Math. Sci. 8 (2010), no. 2, 627-637. link
91. Convergence of nonlocal threshold dynamics approximations to front propagation (with L. Caffarelli), Arch. Ration. Mech. Anal. 195 (2010), no. 1, 1-23. link
90. Asymmetric potentials and motor effect: a homogenization approach (with B. Perthame), Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, 2055-2071. link
89. A discussion about the homogenization of moving fronts (with P. Cardaliaguet and P.-L. Lions), J. Math. Pure Appl. 91 (2009), no. 4, 339-363.link
88. Asymmetric potentials and motor effect: a large deviation approach (with B. Perthame), Arch. Ration. Mech. Anal. 193 (2009), no. 1, 153-169. link
87. Asymptotic and numerical homogenization (with B. Engquist), Acta Numer. 17 (2008), 147-190. link
86. Ergodic problems and periodic homogenization for fully nonlinear equations in half-space domains with Neumann boundary conditions (with G. Barles, F. Da Lio and P.-L. Lions), Indiana Univ. Math. Journal 57 (2008), no. 5, 2355-2376. link
85. A rate of convergence for monotone finite difference approximations to fully nonlinear uniformly elliptic pde (with L. Caffarelli), Comm. Pure Appl. Math. 61 (2008), no. 1, 1-17. link
84. Recent developments in the theory of homogenization for fully nonlinear first- and second-order pde in random environments, Boletín de la Sociedad Española de Matemática Aplicada 34 (2006), 81-90.
83. Homogenization of degenerate second-order pde in periodic and almost periodic environments and applications (with P.-L. Lions), Ann. Inst. H. Poincare, Anal. Non Lineaire, 22 (2005), no. 5, 667-677. link
82. Large time behavior for viscous and non-viscous Hamilton-Jacobi equations forced by additive noise (with N. Dirr), SIAM J. Math. Anal. 37 (2005), no. 3, 777-796. link
81. Front propagation for a jump process arising in spatial ecology (with B. Perthame), Discrete Contin. Dyn. Syst. 13 (2005), no. 5, 1235-1246. link
80. Homogenization for "viscous" Hamilton-Jacobi equations in stationary ergodic media (with P.-L. Lions), Comm. Partial Differential Equations 30 (2005), no. 1-3, 335-376. link
79. Homogenization for fully nonlinear, second-order elliptic and parabolic partial differential equations in stationary ergodic media (with L. Caffarelli and L. Wang), Comm. Pure Appl. Math. 58 (2005), no. 3, 319-361. link
78. Dissipative and entropy solutions to non-isotropic degenerate parabolic balance laws (with B. \ Perthame), Arch. Ration. Mech. Anal. 170 (2003), no. 4, 359-370. link; Attendum to: "Dissipative and entropy solutions to non-isotropic degenerate parabolic balance laws" [Arch. Ration. Mech. Anal. 170 (2003), no. 4, 359--370] (with B. Perthame), Arch. Ration. Mech. Anal. 204 (2004), no. 3, 443-447. link
77. Uniqueness of motion by mean curvature perturbed by stochastic noise (with N. Yip), Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004), no. 1, 1-23. link
76. Correctors for the homogenization theory of Hamilton-Jacobi equations (with P.-L. Lions), Comm. Pure Appl. Math. 56 (2003), no. 10, 1501-1524.link
75. Recent developments in the theory of front propagation and its applications, Modern methods in scientific computing and applications (Montreal, QC, 2001), 397-449, NATO Sci. Ser. II Math. Phys. Chem., 75, Kluwer Acad. Publ., Dordrecht, 2002.
74. Viscosity solutions of fully nonlinear stochastic partial differential equations, Viscosity solutions of differential equations and related topics (Japanese) Kyoto, 2001 Surikaisekikenky Kokyuroku 1287 (2002) 58-65.
73. Some counterexamples on the asymptotic behavior of the solutions of Hamilton-Jacobi equations (with G. Barles), C.R. Acad. Sci. Paris Ser. I Math 330 (2000), no. 11, 963-968. link
72. Equations aux derivees partielles stochastiques nonlineaires et solutions de viscosite (with P.-L. Lions), Seminaire: Equations aux Derivees Partielles, 1998-1999, Exp. No. I, Semin. Equ. Deriv. Partielles, Ecole Polytech., Pallaiseau, 1999.
71. Space-time periodic solutions and long-time behavior of solutions to quasilinear parabolic equations (with G. Barles), SIAM J. Math. Anal. 32 (2001), no. 6, 1311-1323. link
70. Fully nonlinear stochastic partial differential equations with semilinear stochastic dependence (with P.-L. Lions), C. R. Acad. Paris Ser. I Math. 331 (2000), no. 8, 617-624. link
69. Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations (with P.-L. Lions). C. R. Acad. Paris Ser. I Math. 331 (2000), no. 10, 783-790. link
68. Stochastic homogenization for Hamilton-Jacobi equations and applications, Asymptot. Anal. 20 (1999), no. 1, 1-11.
67. On the large time behavior of solutions Hamilton-Jacobi equations (with G. Barles), SIAM J. Math. Anal. 31 (2000), no. 4, 925-939. link
66. The effect of turbulence on mixing in prototype reaction diffusion systems (with A. Majda). Comm. Pure Appl. Math. 53 (2000), no. 10, 1284-1304. link
65. Fully nonlinear stochastic partial differential equations: non-smooth equations and applications (with P. L. Lions). C.R. Acad. Sci. Paris Ser. I 327 (1998), no. 8, 735-741. link
64. Finite volume schemes for Hamilton-Jacobi equations (with G. Kossioris and Ch. Makridakis). Numer. Math. 83 (1999), no. 3, 427-442. link
63. A limiting case for the averaging lemma motivated by the kinetic formulation of some classical systems in fluid mechanics (with B. Perthame), Dynamical systems, plasma and gravitation (Orleans La Source. 1997) 55-61, Lect. Notes in Phys., 518, Springer, Berlin, 1999. link
62. Flame fronts in turbulent combustion models with fractal velocity fields (with A. J. Majda), Comm. Pure Appl. Math 51 (1998), no. 11-12, 1337-1348. link
61. Un cas limite des lemmes de compacite en moyenne motive par la formulation cinetique de systemes hyperbolique (French) (with B. Perthame), Journees "Equations aux Derivees Partielles" (Saint Jean-de-Monts) (1997), Exp. No. XII, Ecole Polytech., Palaiseau, 1997.
60. Remarks on the Dirichlet problem for quasilinear elliptic and parabolic equations (with G. Barles and E. Rouy). Stochastic analysis, control, optimization and applications, 209-222, Systems Control Found. Appl., Birkhauser, Boston, Boston, MA, 1999.
59. A limiting case for velocity averaging (with B. Perthame), Ann. Sci. \'Ecole. Norm. Sup. (4) 31, no. 4, (1998), 591-598. link
58. Fully nonlinear stochastic partial differential equations (with P.-L. Lions), C.R. Acad. Sci. Paris Ser. I Math {b>326 (1998), no. 9, 1085-1092. link
57. Two-player, zero sum differential games and viscosity solutions, Stochastic and differential games, 69-104, Ann. Internat. Soc. Dynam. Games, 4, Birkhäuser Boston, Boston, MA, 1999.
56. Threshold dynamics type approximation schemes for propagating fronts (with H. Ishii and G. Pires). J. Math. Soc. Japan 51 (1999), no. 2, 267-308. link
55. Examples and counterexamples for Huygens principle in premixed combustion (with P. Embid and A. Majda), Combust. Sci. Tech. 120 (1996) 273-303. link
54. A new approach to generalized front propagation problems: theory and applications (with G. Barles). Arch. Ration. Mech. Anal. 141 (1998), no. 3, 237-296. link
53. Stochastic Ising models and anisotropic front propagation (with M. Katsoulakis), J. Stat. Phys. 87 (1997), no. 1-2, 63-89. link
52. Front propagation: Theory and Applications. Viscosity solutions and applications (Montecatini Terme, 1995), Lecture Notes in Math., 1660, Springer, Berlin, 1997. link
51. Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields (with A. Majda), J. Stat. Phys. {\bf 83} (1996) 933-954. link
50. Interface dynamics in phase transitions. Proceedings of the International Congress of Mathematicians, Vol. 1,2 (Zurich, 1994), 1133-1144, Birkhäuser, Basel, (1995).
49. Weak stability of isentropic gas dynamics system for $\gamma =5/3$ (with P. L. Lions and B. Perthame), Progress in elliptic and parabolic partial differential equation (Capri, 1994), 184-192, Pitman Res. Notes Math. Ser., 350, Longman, Harlow, 1996.
48. Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates (with P.-L. Lions and B. Perthame). Comm. Pure Appl. Math. 49, no. 6. (1996) 599-638. link
47. Front propagation for reaction-diffusion arising in combustion theory (with G. Barles and C. Georgelin). Asymptot. Anal. 14 (1997), no. 3, 277-292.
46. Comparison of turbulent flame speeds from complete averaging and the $G$-equation (with P. Embid and A. Majda). Phys. of Fluids 7 (1995), no. 8, 2052-2060. link
45. Effective geometric front dynamics for premixed turbulent combustion with separated velocity scales (with P. Embid and A. Majda). Comb. Sci. Tech. 103 (1995) 85-115. link
44. Generalized motion by mean curvature as a macroscopic limit for stochastic Ising models with long range interactions and Glauber dynamics (with M. Katsoulakis), Comm. Math. Physics 169 (1995), no. 1, 61-97. link
43. Phase field theory for a FitzHugh-Nagumo-type systems (with P. Soravia), SIAM J. Math. Anal. 42 (1996), no. 5, 1341-1359. link
42. Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensors (with H. Ishii), Tohuko Math. J., (2) 47 (1995), no. 2, 227-250. link
41. Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi (with P.-L. Lions). Numer. Math. 69 (1995), no. 4, 441-470. link
40. Anisotropic motion of an interface relaxed by the formation of infinitesimal wrinkles (with M. Gurtin and H.M. Soner). J. Differential Equations 119 (1995), no. 1, 54-108. link
39. A remark on the asymptotic behavior of the solution of the KPP equation (with G. Barles). C.R. Acad. Sci. Paris, S\'er. I Math. 319 (1994), no. 7, 679-684.
38. Large-scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales (with A. Majda). Nonlinearity 7 (1994), no. 1, 1-30. link
37. Interacting particle systems and generalized evolution of fronts (with M. Katsoulakis). Arch. Rational Mech. Anal. 127 (1994), no. 2, 133-157. link
36. Fully nonlinear second-order degenerate elliptic equations with large zeroth-order term (with P.-L. Lions). Indiana Univ. Math. J. 42 (1993), no. 4, 1525-1543. link
35. Front propagation and phase field theory (with G. Barles and H.M. Soner). SIAM J. Control Optim. 31 (1993), no. 2, 439-469. link
34. Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature (with H.M. Soner). Comm. Partial Differential Equations 18 (1993), no. 5-6, 859-894. link
33. Phase transitions and generalized motion by mean curvature (with L.C. Evans and H.M. Soner). Comm. Pure Appl. Math. 45 (1992), no. 9, 1097-1123. link
32. Front propagation for reaction-diffusion equations of bistable type (with L. Bronsard and G. Barles). Ann. Inst. H. Poincar\'e Anal. Non Lineaire 9 (1992), no. 5, 479-496.
31. Convergence of MUSCL type methods for scalar conservation laws (with P.-L. Lions). C.R. Acad. Sci. Paris S\'erie I Math. 311 (1990), no. 5, 259-264.
30. Convergence of approximation schemes for fully nonlinear second order equations (with G. Barles). Asymptotic Anal. 4 (1991), no. 3, 271-283.
29. Instability of a class of dispersive solitary waves (with W.A. Strauss). Proc. Roy. Soc. Edinburgh Sect. A 114 (1990), no. 3-4, 195-212.
28. Wavefront propagation for reaction-diffusion systems of PDE (with G. Barles and L.C. Evans), Duke Math. J. 61 (1990), no. 3, 835-858. link
27. On nonlinear equations of evolution (with M.G. Crandall), Nonlinear Anal. 13 (1989), no. 12, 1375-1392. link
26. A PDE approach to certain large deviations problem for systems of parabolic equations (with L.C. Evans). Analyse non lineaire (Perpignan, 1987). Ann. Inst. H. Poincare Anal. Non Lineaire 6 (1989), suppl., 229-258.
25. A PDE approach to geometric optics for certain reaction-diffusion equations (with L.C. Evans), Indiana Univ. Math. J. 38 (1989), no. 1, 141-172. link
24. On the existence of value functions of two player, zero-sum stochastic differential games (with W.H. Fleming). Indiana Univ. Math. J. 38 (1989), no. 2, 293-314. link
23. Maximal solutions and universal bounds for some partial differential equations of evolution (with M.G. Crandall and P.-L. Lions), Arch. Rational Mech. Anal. 105 (1989), no. 2, 163-190. link
22. Two player, zero-sum stochastic differential games (with W.H. Fleming). Analyse mathematique et applications, 151-164, Gauthier-Villars, Montrouge, 1988.
21. A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations (with R. Jensen and P.-L. Lions), Proc. Amer. Math. Soc. 102, (1988), no. 4, 975-978. link
20. Viscosity solutions of second-order equations, stochastic control and stochastic differential games (with P.-L. Lions), Stochastic differential systems, stochastic control theory and applications (Minneapolis, Minn., 1986), 293-309, IMA Vol. Math. Appl.,10, Springer, New York, 1988.
19. The relation between the porous-medium and eikonal equations in several space dimensions (with P.-L. Lions and J. L. Vazquez), Rev. Mat. Iberoamericana 3 (1987), no. 3-4, 275-310. link
18. Stability and instability of solitary waves of Korteweg-deVries type (with J. L. Bona and W. A. Strauss), Proc. Roy. Soc. Lond. Ser. A 411 (1987), no. 1841, 395-412. link
17. Asymptotic series on the method of vanishing viscosity (with W.H. Fleming), Indiana Univ. Math. J. 35 (1986), no. 2, 425-448. link; Erratum: Indiana Univ. Math. J. 35 (1986), no. 4, 925. link
16. Blow-up of solutions of Hamilton-Jacobi equations (with A. Friedman), Comm. Partial Differential Equations 11 (1986), no. 4, 397-443. link
15. A regularity result for viscosity solutions of Hamilton-Jacobi equations in one space dimension (with R. Jensen), Trans. Amer. Math. Soc. 301 (1987), no. 1, 137-147. link
14. Recent developments in the theory of nonlinear scalar first and second order partial differential equations. Dynamics of Infinite Dimensional Systems (Lisbon, 1986), 301-311, NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., 37, Springer, Berlin, 1987.
13. A remark about viscosity solutions on the boundary, Proc. Amer. Math. Soc. 96 (1986), no. 2, 323-330. link
12. Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' equations, II (with P.-L. Lions), SIAM J. Control Optim. 24 (1986), no. 5, 1086-1089. link
11. PDE-viscosity solution approach to some problems of large deviations (with W.H. Fleming), Ann. di Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1986), no. 2, 171-192. link
10. Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' equations (with P.-L. Lions), SIAM J. Control Optim. 23 (1985), no. 4, 566-583. link
9. A PDE approach to asymptotic estimates for optimal exit probabilities (with W. H. Fleming). Stochastic differential systems (Marseille-Luminy, 1984), 281--285, Lecture Notes in Control and Inform. Sci., 69, Springer, Berlin, 1985.
8. Convergence of difference approximations of quasilinear evolution equations (with M.G. Crandall), Nonlinear Anal. 10 (1986), no. 5, 425-446. link
7. Asymptotic series for solutions to the dynamic programming equation for diffusions with small noise (with W.H. Fleming), Proceeding of 24th IEEE Conference on Decision and Control, December 1985.
6. Max-min representations and product formulas for viscosity solutions of Hamilton-Jacobi equations with applications to differential games, Nonlinear Anal. 9 (1985), no. 3, 217-257. link
5. Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. Differential Equations, 59 (1985), no. 1, 1-43. link
4. Existence of viscosity solutions of Hamilton-Jacobi equations, J. Differential Equations, 56 (1985), no. 3, 345-390. link
3. A PDE approach to some large deviations problems (with W. H. Fleming). Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 441--447, Lectures in Appl. Math. 23, Amer. Math. Soc., Providence, RI, 1986.
2. Developments in the theory of nonlinear first-order partial differential equations (with M.G. Crandall), Differential Equations, Birmingham, Alabama, 1983, 131-142, North-Holland Math. Studies, 92, North-Holland, Amsterdam, 1984.
1. Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations (with L. C. Evans), Indiana U. Math. J. 33 (1984), no. 5, 773-797. link