Fast diffusion equations: Matching large time asymptotics by relative entropy methods

Jean Dolbeault; Giuseppe Toscani

doi:10.3934/krm.2011.4.701

Article Contents

2011, Volume 4, Issue 3: 701-716. Doi: 10.3934/krm.2011.4.701

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Fast diffusion equations: Matching large time asymptotics by relative entropy methods

Jean Dolbeault^1, and
Giuseppe Toscani^2,

1.
Ceremade (UMR CNRS no. 7534), Université Paris Dauphine, Place de Lattre de Tassigny, 75775 Paris Cédex 16
2.
Department of Mathematics at the University of Pavia, via Ferrata 1, 27100 Pavia

Received: May 2010

Revised: June 2011

Published: September 2011

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Abstract

A non self-similar change of coordinates provides improved matching asymptotics of the solutions of the fast diffusion equation for large times, compared to already known results, in the range for which Barenblatt solutions have a finite second moment. The method is based on relative entropy estimates and a time-dependent change of variables which is determined by second moments, and not by the scaling corresponding to the self-similar Barenblatt solutions, as it is usually done.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35K55, 39B62.

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