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Solutions for the two-phase Stefan problem with the Gibbs–Thomson Law for the melting temperature

Published online by Cambridge University Press:  16 July 2009

Stephan Luckhaus
Stephan Luckhaus
Affiliation:
Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse 6, 5300 Bonn, West Germany
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Abstract

The coupling of the Stefan equation for the heat flow with the Gibbs–Thomson law relating the melting temperature to the mean curvature of the phase interface is considered. Solutions, global in time, are constructed which satisfy the natural a priori estimates. Mathematically the main difficulty is to prove a certain regularity in time for the temperature and the indicator function of the phase separately. A capacity type estimate is used to give an L1 bound for fractional time derivatives.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 2 , June 1990 , pp. 101 - 111
Copyright
Copyright © Cambridge University Press 1990

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