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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

Cannon, J. R., Douglas, J. Jr & Denson Hill, C. 1967 A multi-boundary Stefan problem and the disappearance of phases. J. Mat. Mech. 17, 21–33.Google Scholar
Fasano, A.Primicerio, M. & Kamin, S. 1977 Regularity of weak solutions of one-dimensional two-phase Stefan problems. Ann. di Mat. Pura ed Appl. (IV), CXV, 341–348.CrossRefGoogle Scholar
Friedman, A. 1968 One-dimensional Stefan problems with nonmonotone free boundary. Trans. Amer. Math. Soc. 133, 89–114.CrossRefGoogle Scholar
Gévrey, M. 1913 Sur les équations aux dérivées partielles du type parabolique. J. Math. Pures Appl. 9, 305–475.Google Scholar
Kamenomostskaya, S. L. 1961 On Stefan's problem. Mat. Sb. 53, 489–514 (Russian).Google Scholar
Soward, A. M. 1980 A unified approach to Stefan's problem for spheres and cylinders. Proc. R. Soc. Lond. A373, 13 1–147.Google Scholar
Stewartson, K. & Waechter, R. T. 1976 On Stefan's problem for spheres. Proc. R. Soc. Lond. A348, 415–426.Google Scholar