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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The saddle point property for focusing
selfsimilar solutions in a free boundary problem


Authors: Claude-Michel Brauner, Josephus Hulshof and Claudine Schmidt-Lainé
Journal: Proc. Amer. Math. Soc. 127 (1999), 473-479
MSC (1991): Primary 35K55, 35K65, 80A25
MathSciNet review: 1600108
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Abstract: We establish the saddle point property of the focusing selfsimilar solution of a free boundary problem for the heat equation with free boundary conditions given by $u=0$ and ${\partial u\over\partial\nu}=1$.


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Additional Information

Claude-Michel Brauner
Email: brauner@math.u-bordeaux.fr

Josephus Hulshof
Affiliation: Mathématiques Appliquées de Bordeaux, Université Bordeaux I, 33405 Talence cedex, France
Email: hulshof@wi.leidenuniv.nl

Claudine Schmidt-Lainé
Affiliation: CNRS UMR 128, Ecole Normale Supérieure de Lyon, 69364 Lyon cedex 07, France
Email: schmidt@umpa.ens-lyon.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04829-7
PII: S 0002-9939(99)04829-7
Keywords: Free boundary problem, similarity variables, linearization, analytic semigroups, fully nonlinear equations, saddle point property
Received by editor(s): May 21, 1997
Additional Notes: We are grateful for the support of the Universities of Leiden and Bordeaux I and of the HCM-project “Nonlinear PDE-’s" (ERBCHRXCT 940-618). The visit of the first and the third author to Leiden was supported by the ESF/FBP program.
Communicated by: Jeffrey Rauch
Article copyright: © Copyright 1999 American Mathematical Society