Existence of stochastic entropy solutions for stochastic scalar balance laws with Lipschitz vector fields

TL;DR

This paper establishes the existence of stochastic entropy solutions for scalar stochastic balance laws with Lipschitz vector fields, using BGK approximation and generalized Itô formula, including applications to Buckley-Leverett equations.

Contribution

It introduces a novel proof technique for existence of stochastic entropy solutions for scalar laws with Lipschitz vector fields, extending to Buckley-Leverett equations.

Findings

Existence of stochastic entropy solutions proven for scalar stochastic balance laws.

Application of BGK approximation and generalized Itô formula in the proof.

Existence results extended to Buckley-Leverett type equations.

Abstract

In this paper, we consider a scalar stochastic balance law and gain the existence for stochastic entropy solutions. Our proof relies on the BGK approximation and the generalized It\^{o} formula. Moreover, as an application, we derive the existence of stochastic entropy solutions for stochastic Buckley-Leverett type equations.