论文标题
关于两阶段的分数Stefan问题
On the two-phase fractional Stefan problem
论文作者
论文摘要
经典的Stefan问题是研究最多的演化类型的自由边界问题之一。最近，人们有兴趣通过非局部扩散处理相应的自由边界问题。 我们通过审查对我们感兴趣的经典问题的主要特性开始论文。然后，我们介绍了分数Stefan问题并发展基本理论。之后，我们将注意力集中在自我类似的解决方案上，它们的特性和后果。我们首先讨论了作者最近研究的一阶段分数Stefan问题的结果。最后，我们解决了包含本文的主要原始贡献的两阶段分数问题的理论。严格的数值研究支持我们的结果和主张。
The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing the main properties of the classical problem that are of interest for us. Then we introduce the fractional Stefan problem and develop the basic theory. After that we center our attention on selfsimilar solutions, their properties and consequences. We first discuss the results of the one-phase fractional Stefan problem which have recently been studied by the authors. Finally, we address the theory of the two-phase fractional Stefan problem which contains the main original contributions of this paper. Rigorous numerical studies support our results and claims.
