Invariant measures for stochastic conservation laws with Lipschitz flux in the space of almost periodic functions

Abstract

We study the well-posedness of the initial value problem and the long-time behavior of almost periodic solutions to stochastic scalar conservation laws in any space dimension, under the assumption of Lipschitz continuity of the flux functions and a non-degeneracy condition. We show the existence and uniqueness of an invariant measure in a separable subspace of the space of Besicovitch almost periodic functions.