A Bhatnagar-Gross-Krook Approximation to Stochastic Scalar Conservation Laws

Abstract

We study a BGK-like approximation to hyperbolic conservation laws forced by a multiplicative noise. First, we make use of the stochastic characteristics method and establish the existence of a solution for any fi xed parameter \(\varepsilon\). In the next step, we investigate the limit as \(\varepsilon\) tends to 0 and show the convergence to the kinetic solution of the limit problem.