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Self-similar solutions of the p-Laplace heat equation: the case when p > 2

Published online by Cambridge University Press:  13 March 2009

Marie Françoise Bidaut-Véron
Marie Françoise Bidaut-Véron
Affiliation:
Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Faculté des Sciences, Parc Grandmont, 37200 Tours, France (veronmf@univ-tours.fr)
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Abstract

We study the self-similar solutions of the equation

in ℝN, when p > 2. We make a complete study of the existence and possible uniqueness of solutions of the form

of any sign, regular or singular at x = 0. Among them we find solutions with an expanding compact support or a shrinking hole (for t > 0), or a spreading compact support or a focusing hole (for t < 0). When t < 0, we show the existence of positive solutions oscillating around the particular solution .

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 1 , February 2009 , pp. 1 - 43
Copyright
Copyright © Royal Society of Edinburgh 2009

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