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Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient term

Published online by Cambridge University Press:  14 November 2011

S. Snoussi ,
S. Tayachi  and
F. B. Weissler
S. Snoussi
Affiliation:
Département de Mathématiques, Faculté des Sciences de Bizerte, Université Tunis II, Jarzouna 7021, Bizerte, Tunisia, (seifeddine.snoussi@fsb.rnu.tn)
S. Tayachi
Affiliation:
Département de Mathématiques, Faculté des Sciences de Tunis, Université Tunis II, Campus Universitaire, 1060 Tunis, Tunisia (slim.tayachi@fst.rnu.tn)
F. B. Weissler
Affiliation:
Laboratoire Analyse Géométrie et Applications, UMR CNRS 7539, Institut Galilée, Université Paris-Nord 93430 Villetaneuse, France (weissler@math.univ-paris13.fr)
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Extract

We study the existence and the asymptotic behaviour of global solutions of the semilinear parabolic equation u(0) = ϧwhere a, b ∈ℝ, q > 1, p > 1. Forq=2p/(p+1) and ½ 1(p-1)>1 (equivalently, q > (n + 2)/(n + 1)), we prove the existence of mild global solutions for small initial data with respect to some norm. Some of those solutions are asymptotically self-similar.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 6 , 1999 , pp. 1291 - 1307
Copyright
Copyright © Royal Society of Edinburgh 1999

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