Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T21:43:04.844Z Has data issue: false hasContentIssue false

The Stefan problem: continuity of the interfaces for solutions with finite lapnumber

Published online by Cambridge University Press:  14 November 2011

M. H. A. Klaver
Affiliation:
Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands

Synopsis

In this paper we consider the Stefan problem with a heating term. We study the continuity of the interfaces between the mush, the liquid and the solid for solutions of finite lapnumber.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Aronson, D. G., Crandall, M. G. and Peletier, L. A.. Stabilization of solutions of a degenerate nonlinear diffusion problem. Nonlinear Anal. 6 (1982), 10011022.CrossRefGoogle Scholar
2Atthey, D. R.. A finite difference scheme for melting problems. J. lnst. Math. Appl. 13 (1974), 353366.CrossRefGoogle Scholar
3Bertsch, M. and Klaver, M. H. A.. The Stefan problem with mushy regions: continuity of the interface. Proc. Roy. Soc. Edinburgh Sect. A 112 (1989), 3352.CrossRefGoogle Scholar
4Bertsch, M., de Mottoni, P. and Peletier, L. A.. Degenerate diffusion and the Stefan problem. Nonlinear Anal. 8 (1984), 13111336.CrossRefGoogle Scholar
5Ding, Z. Z. and Ughi, M.. A model problem for the diffusion of oxygen in living tissues. Boll. Un.Mat. Ital. B 7 (1987), 111127.Google Scholar
6Matano, H.. Nonincrease of the lapnumber of a solution for a one-dimensional semi-linear parabolic equation. Pub. Sci. Univ. Tokyo, Sec. 1A 29 (1982), 401441.Google Scholar
7Meirmanov, A. M.. An example of nonexistence of a classical solution of the Stefan problem. Soviet Math. Dokl. 23 (1981), 564566.Google Scholar