Large time behaviour of solutions to nonhomogeneous diffusion equations
Volume 74 / 2006
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.
