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

Toscani, Giuseppe; Dolbeault, Jean (2011), Fast diffusion equations: matching large time asymptotics by relative entropy methods, Kinetic and Related Models, 4, 3, p. 701-716. http://dx.doi.org/10.3934/krm.2011.4.701

Type
Article accepté pour publication ou publié
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http://hal.archives-ouvertes.fr/hal-00482898/fr/
Date
2011
Nom de la revue
Kinetic and Related Models
Volume
4
Numéro
3
Éditeur
American Institute of Mathematical Sciences
Pages
701-716
Identifiant publication
Métadonnées
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Auteur(s)
Toscani, Giuseppe
Dolbeault, Jean cc
Résumé (EN)
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.
Mots-clés
asymptotic expansion; second moment; sharp rates; intermediate asymptotics; Fast diffusion equation; porous media equation; Barenblatt solutions; Hardy-Poincaré inequalities; large time behaviour; optimal constants