Large time behaviour of solutions to nonhomogeneous diffusion equations

• Autorzy: Jean Dolbeault , Grzegorz Karch
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 35E05: Fundamental solutions
• 76R50: Diffusion
• 35K05: Heat equation
• 94A17: Measures of information, entropy
• 76S05: Flows in porous media; filtration; seepage
• 35B40: Asymptotic behavior of solutions
• 35K65: Degenerate parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 74
• Numer: 1
• Strony: 133-147

Daty

wydano

2006

Twórcy

autor

Jean Dolbeault

• Ceremade (UMR CNRS no. 7534), Université Paris Dauphine, Place de Lattre de Tassigny, 75775 Paris Cédex 16, France

autor

Grzegorz Karch

• Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/bc74-0-8