Poincaré inequalities for linearizations of very fast diffusion equations

J. A. Carrillo*, C. Lederman, P. A. Markowich, G. Toscani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

In this paper we investigate the large-time asymptotic of linearized very fast diffusion equations with and without potential confinements. These equations do not satisfy, in general, logarithmic Sobolev inequalities, but, as we show by using the 'Bakry-Emery reverse approach', in the confined case they have a positive spectral gap at the eigenvalue zero. We present estimates for this spectral gap and draw conclusions on the time decay of the solution, which we show to be exponential for the problem with confinement and algebraic for the pure diffusive case. These results hold for arbitrary algebraically large diffusion speeds, if the solutions have the mass-conservation property.

Original languageEnglish (US)
Pages (from-to)565-580
Number of pages16
JournalNonlinearity
Volume15
Issue number3
DOIs
StatePublished - May 2002
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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