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

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...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2016-04, Vol.146 (2), p.309-324
Main Authors: Fila, Marek, Winkler, Michael
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Convergence
Diffusion
Diffusion rate
Extinction
Mathematical analysis
Mathematics
Nonlinear equations
Optimization
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Summary: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210515000554