The growth of the second moments of the solutions of fast di↵usion 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 limit. Coming back to original variables, the best matching Barenblatt profile is delayed compared to the self-similar solution with same initial second moment as the initial datum. Such a delay is a new phenomenon, which has to be taken into account for instance when fitting experimental data.

Best matching Barenblatt profiles are delayed

TOSCANI, GIUSEPPE
2015

Abstract

The growth of the second moments of the solutions of fast di↵usion 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 limit. Coming back to original variables, the best matching Barenblatt profile is delayed compared to the self-similar solution with same initial second moment as the initial datum. Such a delay is a new phenomenon, which has to be taken into account for instance when fitting experimental data.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11571/990797
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact