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Disappearance of phase in the Stefan problem: one space dimension

Published online by Cambridge University Press:  16 July 2009

D. G. Aronson  and
S. Kamin
D. G. Aronson
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
S. Kamin
Affiliation:
School of Mathematical Sciences, The Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
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Abstract

We consider the two-phase one-dimensional Stefan problem in a finite interval, with initial and boundary conditions such that the solid phase vanishes at a finite time T and at a single point. We show that the temperature in the solid phase decreases to zero and is bounded by c exp (α/(t − T)) as extinction approaches (C, α > 0) and that phase boundaries at extinction have finite speeds.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 4 , December 1990 , pp. 301 - 309
Copyright
Copyright © Cambridge University Press 1990

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References

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