Some criteria for the disappearance of the mushy region in the Stefan problem

Authors:
I. G. Götz and B. Zaltzman

Journal:
Quart. Appl. Math. **53** (1995), 657-671

MSC:
Primary 35R35; Secondary 35K05, 80A22

DOI:
https://doi.org/10.1090/qam/1359501

MathSciNet review:
MR1359501

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Abstract: The disappearance of the mushy region in a multidimensional one-phase Stefan problem is discussed. In the case of a piecewise-smooth boundary of the domain and bounded initial-boundary data, sufficient conditions for the disappearance of the mushy zone in a finite time are presented. For a -smooth boundary and appropriately smooth boundary data both necessary and sufficient conditions for the mush to vanish are obtained. Possible behaviors of the transient phase for a twodimensional solution near a corner point of the domain are also investigated.

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DOI:
https://doi.org/10.1090/qam/1359501

Article copyright:
© Copyright 1995
American Mathematical Society