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On the stability of some solutions of the Stefan problem†

Published online by Cambridge University Press:  16 July 2009

Riccardo Ricci  and
Xie Weiqing
Riccardo Ricci
Affiliation:
Dipartimento di Matematica, Universita di Milano, Via C. Saldini, 50-20133 Milano, Italy
Xie Weiqing
Affiliation:
Department of Mathematics, University of Pittsburgh, USA
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Abstract

We investigate the stability of travelling wave solutions of the one-dimensional under-cooled Stefan problem. We find a necessary and sufficient condition on the initial datum under which the free boundary is asymptotic to a travelling wave front. The method applies also to other types of solutions.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 2 , Issue 1 , March 1991 , pp. 1 - 15
Copyright
Copyright © Cambridge University Press 1991

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