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asymptotic behaviour near extinction

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation
Part of
- Parabolic equations and systems
Marek Fila, Michael Winkler
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 2 / April 2016

Published online by Cambridge University Press:

03 March 2016, pp. 309-324

Print publication:

April 2016
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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.