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

TL;DR

This paper investigates the existence and uniqueness of invariant measures for stochastic degenerate parabolic-hyperbolic equations with Lipschitz flux, focusing on almost periodic solutions and their long-term behavior in Besicovitch spaces.

Contribution

It establishes the well-posedness and invariant measure existence for stochastic equations with Lipschitz flux in almost periodic function spaces, extending previous results to a broader class.

Findings

Existence of a unique invariant measure in Besicovitch almost periodic function space.

Well-posedness of solutions for stochastic degenerate parabolic-hyperbolic equations.

Long-time behavior characterized by invariant measures.

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.