Ergodicity of Stochastic two-phase Stefan problem driven by pure jump L\'evy noise

TL;DR

This paper studies the long-term behavior of a stochastic two-phase Stefan problem influenced by jump Le9vy noise, establishing existence, uniqueness, and ergodicity of solutions, and characterizing stationary measures.

Contribution

It provides the first rigorous analysis of ergodicity and invariant measures for stochastic Stefan problems driven by jump Le9vy noise.

Findings

Existence and uniqueness of strong solutions.

Ergodicity of the stochastic Stefan problem.

Characterization of invariant measures and stationary solutions.

Abstract

In this paper, we consider stochastic two-phase Stefan problem driven by general jump L\'evy noise. We first obtain the existence and uniqueness of the strong solution and then establish the ergodicity of the stochastic Stefan problem. Moreover, we give a precise characterization of the support of the invariant measures which provides the regularities of the stationary solutions of the stochastic free boundary problems.