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

24 Scopus citations


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
Issue number3
StatePublished - May 2002
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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