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

Toscani, Giuseppe; Dolbeault, Jean

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

External document link

http://hal.archives-ouvertes.fr/hal-00482898/fr/

Date

2011

Journal name

Kinetic and Related Models

Volume

Number

Publisher

American Institute of Mathematical Sciences

Pages

701-716

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.

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 constants