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The Stefan problem with mushy regions: continuity of the interface

Published online by Cambridge University Press:  14 November 2011

M. Bertsch  and
M. H. A. Klaver
M. Bertsch
Affiliation:
Dipartimento di matematica, Universitá di Torino, Via Principe Amedeo 8, 10123 Torino, Italy
M. H. A. Klaver
Affiliation:
Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
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Synopsis

In this paper we consider a one-dimensional Stefan problem with a source term. Under the assumption that the initial profile is monotone, we obtain continuity of the free boundaries between the solid, the mushy and the liquid region.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 1-2 , 1989 , pp. 33 - 52
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Aronson, D. G., Crandall, M. G. and Peletier, L. A.. Stabilization of solutions of a degenerate nonlinear diffusion problem. Nonlinear Anal. 6 (1982), 1001–1022.CrossRefGoogle Scholar
2Atthey, D. R.. A finite difference scheme for melting problems. J. Inst. Math. Appl. 13 (1974), 353–366.CrossRefGoogle Scholar
3Bertsch, M., de Mottoni, P. and Peletier, L. A.. Degenerate diffusion and the Stefan problem. Nonlinear Anal. 8 (1984), 1311–1336.CrossRefGoogle Scholar
4Bertsch, M., de Mottoni, P. and Peletier, L. A.. The Stefan problem with heating: appearance and disappearance of the mushy region. Trans. Amer. Math. Soc. 293 (1986), 677–691.CrossRefGoogle Scholar
5Ding, Z. Z. and Ughi, M.. A model problem for the diffusion of oxygen in living tissues (preprint No. 5, Universitá degli Studi di Firenze, Instituto Matematico “Ulisse Dini”, 1984/1985).Google Scholar
6Ladyzenskaja, O. A., Solonnikov, V. A. and Ural'ceva, N. N.. Linear and quasilinear equations of parabolic type (Providence, Rhode Island: American Mathematical Society, 1968).CrossRefGoogle Scholar
7Matano, H.. Nonincrease of the lapnumber of a solution for a one-dimensional semi-linear parabolic equation. Pub. Sci. Univ. Tokyo, Sec. 1A 29 (1982), 401–441.Google Scholar