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Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  03 March 2016

Marek Fila  and
Michael Winkler
Marek Fila
Affiliation:
Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava, Slovakia (fila@fmph.uniba.sk)
Michael Winkler
Affiliation:
Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany (michael.winkler@math.uni-paderborn.de)
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Abstract

We study the asymptotic behaviour of solutions of the fast diffusion equation near extinction. For a class of initial data, the asymptotic behaviour is described by a singular Barenblatt profile. We complete previous results on rates of convergence to the singular Barenblatt profile by describing a new phenomenon concerning the difference between the rates in time and space.

Keywords

fast diffusion equationasymptotic behaviour near extinctionnonlinear Fokker–Planck equation

MSC classification

Primary: 35K55: Nonlinear parabolic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 2 , April 2016 , pp. 309 - 324
Copyright
Copyright © Royal Society of Edinburgh 2016 

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