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IOP Publishing, Journal of Physics A: Mathematical and Theoretical, 6(48), p. 065206

DOI: 10.1088/1751-8113/48/6/065206

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Best matching Barenblatt profiles are delayed

Journal article published in 2015 by Jean Dolbeault ORCID, Giuseppe Toscani
This paper is available in a repository.
This paper is available in a repository.

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Abstract

The growth of the second moments of the solutions of fast diffusion equations is asymptotically governed by the behavior of self-similar solutions. However, at next order, there is a correction term which amounts to a delay depending on the nonlinearity and on a distance of the initial data to the set of self-similar Barenblatt solutions. This distance can be measured in terms of a relative entropy to the best matching Barenblatt profile. This best matching Barenblatt function determines a scale. In new variables based on this scale, which are given by a self-similar change of variables if and only if the initial datum is one of the Barenblatt profiles, the typical scale is monotone and has a li