Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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 $ {C^2}$ -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

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