A free boundary problem of Stefan type with nonlocal diffusion
A free boundary problem of Stefan type with nonlocal diffusion
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发表时间：
2018-05
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通讯作者：
Carmen Cort'azar;F. Quir'os;N. Wolanski
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作者：
Carmen Cort'azar;F. Quir'os;N. Wolanski
我们介绍和分析一个非本地版本的单相Stefan问题，其中，在经典模型中，液相的体积的增长率是成比例的能量损失通过相间的速率。我们证明了存在性和唯一性的问题上提出的线上，和半线上的常数Dirichlet数据，并在径向的情况下，在几个维度。我们还描述了解决方案和它的自由边界的渐近行为。该模型可能是感兴趣的，以描述在恶劣的环境中的人口的蔓延。
We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the interphase. We prove existence and uniqueness for the problem posed on the line, and on the half-line with constant Dirichlet data, and in the radial case in several dimensions. We also describe the asymptotic behaviour of both the solution and its free boundary. The model may be of interest to describe the spreading of populations in hostile environments.