A+ CATEGORY SCIENTIFIC UNIT

Large time behaviour of solutions to nonhomogeneous diffusion equations

Volume 74 / 2006

Jean Dolbeault, Grzegorz Karch Banach Center Publications 74 (2006), 133-147 MSC: Primary 35K05, 35K65; Secondary 35B40, 35E05, 94A17, 76S05, 76R50. DOI: 10.4064/bc74-0-8

Abstract

This note is devoted to the study of the long time behaviour of solutions to the heat and the porous medium equations in the presence of an external source term, using entropy methods and self-similar variables. Intermediate asymptotics and convergence results are shown using interpolation inequalities, Gagliardo-Nirenberg-Sobolev inequalities and Csiszár-Kullback type estimates.

Authors

  • Jean DolbeaultCeremade (UMR CNRS no. 7534)
    Université Paris Dauphine
    Place de Lattre de Tassigny
    75775 Paris Cédex 16, France
    e-mail
  • Grzegorz KarchInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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