Uniqueness of stochastic entropy solutions for stochastic balance laws with Lipschitz fluxes

TL;DR

This paper proves the uniqueness of stochastic entropy solutions for stochastic balance laws with Lipschitz fluxes, using stochastic kinetic formulation and regularization, and extends results to porous media equations.

Contribution

It introduces a novel proof of uniqueness for stochastic entropy solutions with Lipschitz fluxes and applies it to stochastic porous media equations.

Findings

Uniqueness of stochastic entropy solutions established.

Method combines stochastic kinetic formulation and Itô calculus.

Results applicable to stochastic porous media equations.

Abstract

In this paper, we consider a stochastic balance law with a Lipschitz flux and gain the uniqueness for stochastic entropy solutions. The argument is supported by the stochastic kinetic formulation, the It\^{o} formula and the regularization techniques. Furthermore, as an application, we derive the uniqueness of stochastic entropy solutions for stochastic porous media type equations.