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Very slow grow-up of solutions of a semi-linear parabolic equation

Part of: Parabolic equations and systems Partial differential equations

Published online by Cambridge University Press:  30 March 2011

Marek Fila ,
John R. King ,
Michael Winkler  and
Eiji Yanagida
Marek Fila
Affiliation:
Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava, Slovakia ([email protected])
John R. King
Affiliation:
Division of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD, UK ([email protected])
Michael Winkler
Affiliation:
Fachbereich Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany ([email protected])
Eiji Yanagida
Affiliation:
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan ([email protected])
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Abstract

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We consider large-time behaviour of global solutions of the Cauchy problem for a parabolic equation with a supercritical nonlinearity. It is known that the solution is global and unbounded if the initial value is bounded by a singular steady state and decays slowly. In this paper we show that the grow-up of solutions can be arbitrarily slow if the initial value is chosen appropriately.

Keywords

grow-upsemi-linear parabolic equationcomparison principle

MSC classification

Secondary: 35K57: Reaction-diffusion equations 35B40: Asymptotic behavior of solutions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 381 - 400
Copyright
Copyright © Edinburgh Mathematical Society 2011

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