Ergodicity for stochastic conservation laws with multiplicative noise

TL;DR

This paper establishes the existence and uniqueness of an invariant measure for stochastic conservation laws with multiplicative noise, demonstrating polynomial mixing in a weighted L^1 space, advancing understanding of long-term behavior of such systems.

Contribution

It proves the existence and uniqueness of invariant measures and polynomial mixing for stochastic conservation laws with multiplicative noise, using kinetic solutions in weighted L^1 spaces.

Findings

Unique invariant measure exists for the system.

Polynomial mixing property is established.

Results are valid in the kinetic solution framework.

Abstract

We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, a polynomial mixing property is established. This is done in the setting of kinetic solutions taking values in an L^1-weighted space.