European Journal of Applied Mathematics

Table of Contents - 2004 - Volume 15, Issue 03  


Papers

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

D. HILHORST a1, F. ISSARD-ROCH a1 and J. M. ROQUEJOFFRE a2
a1 UMR 8628, Analyse Numérique et EDP, CNRS et Université de Paris-Sud, Bâtiment 425, 91405 Orsay, France
a2 UFR MIG, UMR 5640 Université de Toulouse III, 118, route de Narbonne, 31062 Toulouse, France

Article author query
hilhorst d   [Google Scholar] 
issard-roch f   [Google Scholar] 
roquejoffre jm   [Google Scholar] 
 

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.

(Published Online September 1 2004)
(Received May 14 2002)
(Revised June 23 2003)