Best matching Barenblatt profiles are delayed

Jean Dolbeault (1) , Giuseppe Toscani (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Dipartimento di matematica F. Casorati

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

Mots clés: delay; entropy production method; entropy; Barenblatt profiles; fast diffusion equation; second moment; intermediate asymptotics; self-similar solutions

Domaines: Equations aux dérivées partielles [math.AP]

Jean Dolbeault, Giuseppe Toscani. Best matching Barenblatt profiles are delayed. Journal of Physics A General Physics (1968-1972), 2015, 48 (6), pp.065206, 14. ⟨hal-01058838v2⟩