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

Xiaotian Ge; Shijie Shang; Jianliang Zhai; Tusheng Zhang

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arXiv · 2408.01305

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

Xiaotian Ge·Shijie Shang·Jianliang Zhai·Tusheng Zhang

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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.

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Xiaotian Ge, Shijie Shang, Jianliang Zhai, Tusheng Zhang. 2024-08-02. Ergodicity of Stochastic two-phase Stefan problem driven by pure jump L\'evy noise. https://arxiv.org/abs/2408.01305

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