发表机构
Normandie University, INSA de Rouen Normandie（诺曼底大学，鲁昂国立应用科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究随机Stefan问题在潜热系数趋于零时的极限，通过引入时间白噪声和空间有色噪声，证明了弱解的存在唯一性，并基于正潜热与零潜热解之间的误差估计（即使在确定性情形下也新颖）建立了极限行为。
AI 中文摘要
本文旨在推广Hilhorst、Mimura和Sch{ä}tzle [18]关于生物学中出现的两相Stefan问题在潜热系数趋于零时极限的论文。我们引入一种相当一般的加性噪声，该噪声在时间上为白噪声，在空间上有色，并研究相应的随机Stefan问题的解在潜热系数消失时的极限。我们首先证明该问题弱解的存在唯一性，然后研究解在潜热系数趋于零时的极限。与[18]不同，我们的证明方法基于具有正潜热的Stefan问题的解与具有零潜热的Stefan问题的解之间的误差估计，这一方法即使在未添加噪声的确定性情形下也似乎是新颖的。
英文摘要
The purpose of this paper is to extend an article by Hilhorst, Mimura and Sch{ä}tzle [18] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem arising in biology. We introduce a rather general additive noise white in time and colored in space, and search for the limit of the solution of the corresponding stochastic Stefan problem as the latent heat coefficient vanishes. We first prove the existence and uniqueness of the weak solution of this problem, and then study the limit of the solution as the latent heat coefficient tends to zero. Unlike in [18], our method of proof is based upon an error estimate between the solution of the Stefan problem with positive latent heat and that of the Stefan problem with zero latent heat, which seems to be novel even in the deterministic case when no noise is added.
