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

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

2010-05-12

arxiv.org/abs/1005.1994v2

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

Mathematics

Analysis of PDEs

Scientific paper

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.

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