# Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

## TL;DR

This paper surveys recent progress on the long-term behavior of stochastic nonlinear conservation laws, focusing on invariant measures for second-order degenerate parabolic-hyperbolic equations driven by white noise.

## Contribution

It establishes the existence and uniqueness of invariant measures for these stochastic conservation laws, highlighting recent theoretical advances.

## Key findings

- Existence of invariant measures proven for certain stochastic conservation laws.
- Uniqueness of invariant measures established under specific conditions.
- Discussion of open problems and future research directions.

## 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.