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arXiv : 1005.1994

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Kinetic and related models 4, 3 (2011) 701-716

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v1 (12-05-2010)

v2 (05-05-2011)

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

Jean Dolbeault 1, Giuseppe Toscani 2

(2011)

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.

1 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine
2 :	Department of Mathematics,
	University of Pavia, Italy

Domaine

:

Mathématiques/Equations aux dérivées partielles

Mots Clés : Fast diffusion equation – porous media equation – Barenblatt solutions – Hardy-Poincaré inequalities – large time behaviour – second moment – asymptotic expansion – intermediate asymptotics – sharp rates – optimal constants

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Contributeur : Jean Dolbeault <>

Soumis le : Mercredi 4 Mai 2011, 20:05:59

Dernière modification le : Dimanche 18 Décembre 2011, 18:08:31