On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass

Claudia Lederman*, Peter Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We extend the existing theory on large-time asymptotics for convection-diffusion equations, based on the entropy-entropy dissipation approach, to certain fast diffusion equations with uniformly convex confinement potential and finite-mass but infinite-entropy equilibrium solutions. We prove existence of a mass preserving solution of the Cauchy problem and we show exponential convergence, as t → ∞, at a precise rate to the corresponding equilibrium solution in the L1 norm. As by-product we also derive corresponding generalized Sobolev inequalities.

Original languageEnglish (US)
Pages (from-to)301-332
Number of pages32
JournalCommunications in Partial Differential Equations
Volume28
Issue number1-2
DOIs
StatePublished - Jan 1 2003

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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