Best matching Barenblatt profiles are delayed
Dolbeault, Jean; Toscani, Giuseppe (2015), Best matching Barenblatt profiles are delayed, Journal of Physics. A, Mathematical and Theoretical, 48, 6, p. n°065206. 10.1088/1751-8113/48/6/065206
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1408.6781v2
Journal nameJournal of Physics. A, Mathematical and Theoretical
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Abstract (EN)The growth of the second moments of the solutions of fast diffusionequations 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 thenonlinearity and on a distance of the initial data to the set of self-similar Barenblattsolutions. This distance can be measured in terms of a relative entropy to the bestmatching Barenblatt profile. This best matching Barenblatt function determines ascale. In new variables based on this scale, which are given by a self-similar change ofvariables if and only if the initial datum is one of the Barenblatt profiles, the typicalscale is monotone and has a limit. Coming back to original variables, thebest matchingBarenblatt profile is delayed compared to the self-similar solution withsame initialsecond moment as the initial datum. Such a delay is a new phenomenon, which has tobe taken into account for instance when fitting experimental data.
Subjects / Keywordsfast diffusion equation; intermediate asymptotics; Barenblatt profiles; self-similar solutions; entropy production method; second moment; entropy; delay
Showing items related by title and author.
Lederman, Claudia; Jüngel, Ansgar; Arnold, Anton; Carrillo, José A.; Desvillettes, Laurent; Dolbeault, Jean; Markowich, Peter; Toscani, Giuseppe; Villani, Cédric (2004) Article accepté pour publication ou publié