Invariant measures for stochastic parabolic–hyperbolic equations in the space of almost periodic functions: Lipschitz flux case

Abstract

We study the well-posedness and the long-time behavior of almost periodic solutions to stochastic degenerate parabolic–hyperbolic equations in any space dimension, under the assumption of Lipschitz continuity of the flux and viscosity 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.