Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

Abstract

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white noises. Some further developments, problems, and challenges in this direction are also discussed.

Keywords

Stochastic solutions / Entropy solutions / Invariant measures / Existence / Uniqueness / Stochastic forcing / Anisotropic degenerate / Parabolichyperbolic equations / Long-time behavior

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