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Large time behaviour of solutions to nonhomogeneous diffusion equations

Dolbeault, Jean; Karch, Grzegorz (2006), Large time behaviour of solutions to nonhomogeneous diffusion equations, in Biler, Piotr; Karch, Grzegorz, Self-Similar Solutions of Nonlinear PDE, Banach Center Publications - Institute of Mathematics - Polish Academy of Science, p. 133-147. http://dx.doi.org/10.4064/bc74-0-08

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Type
Communication / Conférence
Date
2006
Conference title
Self-Similar Solutions of Nonlinear PDE
Conference date
2005-09
Conference city
Bedlewo
Conference country
Pologne
Book title
Self-Similar Solutions of Nonlinear PDE
Book author
Biler, Piotr; Karch, Grzegorz
Publisher
Banach Center Publications - Institute of Mathematics - Polish Academy of Science
Pages
133-147
Publication identifier
Metadata
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Author(s)
Dolbeault, Jean cc
Karch, Grzegorz
Abstract (EN)
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.
Subjects / Keywords
Csiszár-Kullback type estimates; Gagliardo-Nirenberg-Sobolev inequalities; interpolation inequalities; porous medium equations