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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-8,
author = {Jean Dolbeault and Grzegorz Karch},
title = {Large time behaviour of solutions to nonhomogeneous diffusion equations},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {133-147},
zbl = {1124.35011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-8}
}
Jean Dolbeault; Grzegorz Karch. Large time behaviour of solutions to nonhomogeneous diffusion equations. Banach Center Publications, Tome 72 (2006) pp. 133-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-8/