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

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 Itô formula. Moreover, as an application, we derive the existence of stochastic entropy solutions for stochastic Buckley-Leverett type equations.

This paper has been withdrawn by the author due to some mistakes in proof of Theorem 3.1