Panagiotis E. Souganidis

Charles H. Swift Distinguished Service Professor
Department of Mathematics
The University of Chicago
5734 S. University Avenue
Chicago, Illinois 606377

email: souganidis@math.uchicago.edu
office: Ryerson 360G

Research Interests

Nonlinear partial differential equations

Publications

105. A homogenization approach for the motion of motor proteins (with S. Mirrahimi), Nonlinear Differential Equatiions and Applications, to appear . arXiv
104. Homogenization and enhancement of the $G$-equation in random environments (with P. Cardaliaguet), preprint. arXiv
103. Homogenization of $L^\infty$ variational problems (with S. Armstrong), preprint. arXiv
102. A pde approach to small stochastic perturbations of Hamiltonian flows (with H. Ishii), J. Differential Equations 252, no. 2, 1748-1775. link
101. Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments (with S. Armstrong), Journal Mathematiques Pure et Appliques, to appear. arXiv | link
100. Singular Hamilton-Jacobi equation for the tail problem (with S. Mirrahimi, G. Barles and B. Perthame), submitted.
99. Homogenization and enhancement for the G-equation in periodic media (with P. Cardaliaguet and J. Nolen), Arch. Ration. Mech. Anal. 199, no. 2, 527-561. link
98. A homogenization approach to flashing ratchets (with B. Perthame), Nonlinear Differential Equations Appl. 18 (2011), no. 1, 45-58. link
97. Rates of convergence for the homogenization of uniformly elliptic pde in random media (with L. Caffarelli), Invent. Math. 180, no. 2, 301-360. link
96. 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
95. 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
94. Convergence of nonlocal threshold dynamics approximations to front propagation (with L. Caffarelli), Arch. Ration. Mech. Anal. 195 (2010), no. 1, 1-23. link
93. Recent developments in the theory of stochastic homogenization of first- and second- order fully nonlinear pde and applications, Bol. Soc. Esp. Mat. Apl. SeMA No. 34 (2006), 81-90.
92. 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
91. 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
90. Asymmetric potentials and motor effect: a large deviation approach (with B. Perthame), Arch. Ration. Mech. Anal. 193 (2009), no. 1, 153-169. link
89. Asymptotic and numerical homogenization (with B. Engquist), Acta Numer. 17 (2008), 147-190. link
88. 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
87. 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
86. 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.
85. 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
84. 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
83. Front propagation for a jump process arising in spatial ecology (with B. Perthame), Discrete Contin. Dyn. Syst. 13 (2005), no. 5, 1235-1246. link
82. 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
81. 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
80. 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
79. 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
78. 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
77. Correctors for the homogenization theory of Hamilton-Jacobi equations (with P.-L. Lions), Comm. Pure Appl. Math. 56 (2003), no. 10, 1501-1524.link
76. 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.
75. 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.
74. 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
73. 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.
72. 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
71. 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
70. 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
69. Stochastic homogenization for Hamilton-Jacobi equations and applications, Asymptot. Anal. 20 (1999), no. 1, 1-11.
68. On the large time behavior of solutions Hamilton-Jacobi equations (with G. Barles), SIAM J. Math. Anal. 31 (2000), no. 4, 925-939. link
67. 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
66. 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
65. Finite volume schemes for Hamilton-Jacobi equations (with G. Kossioris and Ch. Makridakis). Numer. Math. 83 (1999), no. 3, 427-442. link
64. 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
63. 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
62. 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.
61. 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.
60. A limiting case for velocity averaging (with B. Perthame), Ann. Sci. École. Norm. Sup. (4) 31, no. 4, (1998), 591-598. link
59. 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
58. 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.
57. 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
56. Examples and counterexamples for Huygens principle in premixed combustion (with P. Embid and A. Majda), Combust. Sci. Tech. 120 (1996) 273-303. link
55. 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
54. Stochastic Ising models and anisotropic front propagation (with M. Katsoulakis), J. Stat. Phys. 87 (1997), no. 1-2, 63-89. link
53. Front propagation: Theory and Applications. Viscosity solutions and applications (Montecatini Terme, 1995), Lecture Notes in Math., 1660, Springer, Berlin, 1997. link
52. Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields (with A. Majda), J. Stat. Phys. {\bf 83} (1996) 933-954. link
51. Interface dynamics in phase transitions. Proceedings of the International Congress of Mathematicians, Vol. 1,2 (Zurich, 1994), 1133-1144, Birkhäuser, Basel, (1995).
50. 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.
49. 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
48. Front propagation for reaction-diffusion arising in combustion theory (with G. Barles and C. Georgelin). Asymptot. Anal. 14 (1997), no. 3, 277-292.
47. 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
46. 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
45. 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
44. Phase field theory for a FitzHugh-Nagumo-type systems (with P. Soravia), SIAM J. Math. Anal. 42 (1996), no. 5, 1341-1359. link
43. 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
42. 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
41. 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
40. 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.
39. Large-scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales (with A. Majda). Nonlinearity 7 (1994), no. 1, 1-30. link
38. Interacting particle systems and generalized evolution of fronts (with M. Katsoulakis). Arch. Rational Mech. Anal. 127 (1994), no. 2, 133-157. link
37. 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
36. Front propagation and phase field theory (with G. Barles and H.M. Soner). SIAM J. Control Optim. 31 (1993), no. 2, 439-469. link
35. 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
34. 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
33. 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.
32. 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.
31. Convergence of approximation schemes for fully nonlinear second order equations (with G. Barles). Asymptotic Anal. 4 (1991), no. 3, 271-283.
30. 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.
29. 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
28. On nonlinear equations of evolution (with M.G. Crandall), Nonlinear Anal. 13 (1989), no. 12, 1375-1392. link
27. 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.
26. 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
25. 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
24. 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
23. Two player, zero-sum stochastic differential games (with W.H. Fleming). Analyse mathematique et applications, 151-164, Gauthier-Villars, Montrouge, 1988.
22. 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
21. 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.
20. 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
19. 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
18. Erratum: "Asymptotic series and the method of vanishing viscosity'' (with W. H. Fleming), Indiana Univ. Math. J. 35 (1986), no. 4, 925. 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
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