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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00482898/fr/Date
2011Journal name
Kinetic and Related ModelsVolume
4Number
3Publisher
American Institute of Mathematical Sciences
Pages
701-716
Publication identifier
Metadata
Show full item recordAbstract (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.Subjects / Keywords
asymptotic expansion; second moment; sharp rates; intermediate asymptotics; Fast diffusion equation; porous media equation; Barenblatt solutions; Hardy-Poincaré inequalities; large time behaviour; optimal constantsRelated items
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