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.
I. G. Götz and B. Zaltzman, Two-Phase Stefan Problem with Supercooling, preprint (1993)
M. E. Gurtin, Thermodynamics and the Supercritical Stefan Equations with Nucleations, CMU-report (1992)
- Stephan Luckhaus, Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature, European J. Appl. Math. 1 (1990), no. 2, 101–111. MR 1117346, DOI https://doi.org/10.1017/S0956792500000103
- A. Visintin, Stefan problem with a kinetic condition at the free boundary, Ann. Mat. Pura Appl. (4) 146 (1987), 97–122. MR 916689, DOI https://doi.org/10.1007/BF01762361
- Wei Qing Xie, The Stefan problem with a kinetic condition at the free boundary, SIAM J. Math. Anal. 21 (1990), no. 2, 362–373. MR 1038897, DOI https://doi.org/10.1137/0521020
I. G. Götz and B. Zaltzman, Two-Phase Stefan Problem with Supercooling, preprint (1993)
M. E. Gurtin, Thermodynamics and the Supercritical Stefan Equations with Nucleations, CMU-report (1992)
St. Luckhaus, Solutions of the two phase Stefan problem with the Gibbs-Thomson relation for the melting temperature, Europ. J. Appl. Math. 1, 101–111 (1990)
A. Visintin, Stefan problem with a kinetic condition at the free boundary, Annali Mat. Pura Appl. 146, 97–122 (1987)
W. Xie, The Stefan problem with a kinetic condition at the free boundary, SIAM J. Math. Anal. 21, no. 2, 362–373 (1990)
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Article copyright:
© Copyright 1997
American Mathematical Society