Regularization by noise in (2x 2) hyperbolic systems of conservation law

Abstract

In this paper we study a non strictly systems of conservation law by stochastic perturbation. We show the existence and uniqueness of the solution. We do not assume that $BV$-regularity for the initial conditions. The proofs are based on the concept of entropy solution and in the characteristics method (in the influence of noise). This is the first result on the regularization by noise in hyperbolic systems of conservation law.