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

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Date
2011
Link to item file
http://hal.archives-ouvertes.fr/hal-00482898/fr/
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Analyse
Sujet
asymptotic expansion; second moment; sharp rates; intermediate asymptotics; Fast diffusion equation; porous media equation; Barenblatt solutions; Hardy-Poincaré inequalities; large time behaviour; optimal constants
Journal issue
Kinetic and Related Models
Volume
4
Number
3
Publication date
2011
Article pages
701-716
Publisher
American Institute of Mathematical Sciences
DOI
http://dx.doi.org/10.3934/krm.2011.4.701
URI
https://basepub.dauphine.fr/handle/123456789/4268
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Author
Toscani, Giuseppe
Dolbeault, Jean
Type
Article accepté pour publication ou publié
Abstract (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.