Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Convergence of the two-phase Stefan problem to the one-phase problem

Author: Barbara E. Stoth
Journal: Quart. Appl. Math. 55 (1997), 113-126
MSC: Primary 80A22; Secondary 35K05, 35R35
DOI: https://doi.org/10.1090/qam/1433755
MathSciNet review: MR1433755
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Abstract: We study the limit of the one-dimensional Stefan problem as the diffusivity coefficient of the solid phase approaches zero. We derive a weak formulation of the equilibrium condition for the resulting one-phase problem that allows jumps of the temperature across the interface. The weak formulation consists of a regularity condition that only enforces the usual equilibrium condition to hold from the liquid phase.

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DOI: https://doi.org/10.1090/qam/1433755
Article copyright: © Copyright 1997 American Mathematical Society

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