We study the large-time behavior of the solutions to viscous and nonviscous Hamilton-Jacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the...
Dissipative and Entropy Solutions to Non-Isotropic Degenerate Parabolic Balance Laws (2003)
Beno Ît, Benoit Perthame, P.E. Souganidis
We propose a new notion of weak solutions (dissipative solutions) for nonisotropic, degenerate, second order, quasi-linear parabolic equations. This class of solutions is an extension of the notion...
Lions, P.-L., Souganidis, P.E.
Recent work by the authors and others has demonstrated the connections between the dynamic programming approach for two-person, zero-sum differential games and the new notion of viscosity solutions...
Convergence of Difference Approximations of Quasilinear Evolution Equations. (2002)
Crandall,M. G., Souganidis,P. E.
The very successful theory of quasilinear evolution equations, which applies to many problems of mathematical physics, has been developed by T. Kato. The theory obtains solutions of quasilinear...
Recent work by the authors and others has demonstrated the connections between the dynamic programming approach to optimal control theory and to two-person, zero-sum differential games problems and...
Developments in the Theory of Nonlinear First-Order Partial Differential Equations. (1998)
Crandall,M. G., Souganidis,P. E.
The theory of scalar first-order fully nonlinear partial differential equations has recently enjoyed a strong development. One major step was a proof by M. Crandall and P.-L. Lions of the uniqueness...
Wavefront Propagation for Reaction-Diffusion Systems of PDE, (1998)
Barles, G., Evans, L. C., Souganidis, P. E.
The theory of viscosity solutions for Hamilton-Jacobi equations is used to study the asymptotic behavior of solutions to certain systems of reaction-diffusion PDE. Our principal result characterizes...
A Limiting Case for Velocity Averaging (1998)
Uperieure S Ormale, N Ecole, B. Perthame, B. Perthame, B. Perthame, Universit'e P. Et M. Curie, ...
We complete the theory of velocity averaging lemmas for transport equations by studying the limiting case of a full space derivative in the source term. Although the compactness of averages does not...
Convergence of the Optimal Feedback Policies in a. . . (1998)
Paul Dupius, W. H. Fleming, P. E. Souganidis, Asymptotic Series
Introduction to Partial Differential Equations, Princeton University Press, New Jersey, 1976. [18] H. J. Kushner, Probability Methods for Approximations in Stochastic Control and for Elliptic...
P.-L. Lions, P. E. Souganidis
This paper considers the questions of convergence of: (i) MUSCL type (i.e. second-order, TVD) finite-difference approximations towards the entropic weak solution of scalar, one-dimensional...
The Relation Between the Porous Medium and the Eikonal Equations in Several Space Dimensions. (1987)
Souganidis, P.E., Lions, P. L., Vázquez, J.L.
We study the relation between the porous medium equation ut = ?(um), m > 1, and the eikonal equation vt = |Dv|2. Under quite general assumtions, we prove that the pressure and the interface of the...