Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 59, No. 3, pp. 315-323 (2002)

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Stability and Continuous Dependence of Solutions of One-Phase Stefan Problems for Semilinear Parabolic Equations

Philippe Souplet

Département de Mathématiques, Université de Picardie,
INSSET, 02109 St-Quentin -- FRANCE
and
Laboratoire de Mathémati\-ques Appliquées, UMR CNRS 7641, Université de Versailles,
45 avenue des Etats-Unis, 78035 Versailles -- FRANCE
E-mail: souplet@math.uvsq.fr

Abstract: We consider a one-phase Stefan problem for the heat equation with a superlinear reaction term and we prove the stability of fastly decaying global solutions. Also, we establish a result of continuous dependence of local solutions up to the maximum existence time, needed for the stability proof.

Keywords: nonlinear reaction-diffusion equation; free boundary condition; Stefan problem; global existence; stability; continuous dependence.

Classification (MSC2000): 35K55, 35R35, 80A22, 35B35, 35B40.

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Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

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