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Nonlinear Two-Phase Stefan Problem
In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.
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We study a nonlocal version of the one-phase Stefan problem which develops mushy regions, even if they were not present initially, a model which can be of interest at the mesoscopic scale. The equation involves a convolution with a compactly supported kernel. The created mushy regions have the size of the support of this kernel. If the kernel is suitably rescaled, such regions disappear and the...
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One and two phase Stefan problems for the linear heat equation have been the subject of many studies in the past [1, 2]. Indeed these problems have a great physical relevance since they provide a mathematical model for the processes of phase changes [3, 4]. The boundary between the two phases is a free boundary: its motion has to be determined as part of the solution. More recently the previous...
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 1970
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/282082