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Asymptotic behaviour of the solutions of the supercooled Stefan problem
Published online by Cambridge University Press: 14 November 2011
Abstract
In this paper, we prove that the Hele–Shaw problem with kinetic condition and surface tension is the limit case of the supercooled Stefan problem in the classical sense when specific heat ε goes to zero. The method is the use of a fixed-point theorem; the key is to construct a workable function space. The main feature is to obtain the existence and the uniform estimates with respect to ε > 0 at the same time for the solutions of the supercooled Stefan problem. For the sake of simplicity, we only consider the case of one phase, although the method used here is also applicable in the case of two phases.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 1 , 1997 , pp. 181 - 189
- Copyright
- Copyright © Royal Society of Edinburgh 1997
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