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Large time behavior of the solutions to a one-dimensional Stefan problem with a kinetic condition at the free boundary

Published online by Cambridge University Press:  01 September 2004

D. HILHORST ,
F. ISSARD-ROCH  and
J. M. ROQUEJOFFRE
D. HILHORST
Affiliation:
UMR 8628, Analyse Numérique et EDP, CNRS et Université de Paris-Sud, Bâtiment 425, 91405 Orsay, France
F. ISSARD-ROCH
Affiliation:
UMR 8628, Analyse Numérique et EDP, CNRS et Université de Paris-Sud, Bâtiment 425, 91405 Orsay, France
J. M. ROQUEJOFFRE
Affiliation:
UFR MIG, UMR 5640 Université de Toulouse III, 118, route de Narbonne, 31062 Toulouse, France
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Abstract

We consider a Stefan problem with a kinetic condition at the free boundary and prove the convergence of the solution as $t$ tends to infinity either to a travelling wave solution or to a self-similar solution. The key idea is to transform this problem into a problem for a single nonlocal parabolic equation which admits a comparison principle.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 15 , Issue 3 , June 2004 , pp. 297 - 313
Copyright
2004 Cambridge University Press

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