We study a generalization of the porous medium equation involving nonlocal terms. More precisely, explicit self-similar solutions with compact support generalizing the Barenblatt solutions are constructed. We also present a formal argument to get the decay of weak solutions of the corresponding Cauchy problem.
Cette Note est consacrée à lʼétude dʼune généralisation non locale de lʼéquation des milieux poreux. Plus précisément, on obtient des formules explicites de solutions auto-similaires à support compact qui ressemblent fortement aux solutions de type Barenblatt. On donne aussi un argument formel qui permet dʼobtenir des estimations des solutions faibles du problème de Cauchy.
Accepted:
Published online:
Biler, Piotr 1 ; Imbert, Cyril 2 ; Karch, Grzegorz 1
@article{CRMATH_2011__349_11-12_641_0,
author = {Biler, Piotr and Imbert, Cyril and Karch, Grzegorz},
title = {Barenblatt profiles for a nonlocal porous medium equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {641--645},
year = {2011},
publisher = {Elsevier},
volume = {349},
number = {11-12},
doi = {10.1016/j.crma.2011.06.003},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2011.06.003/}
}
TY - JOUR AU - Biler, Piotr AU - Imbert, Cyril AU - Karch, Grzegorz TI - Barenblatt profiles for a nonlocal porous medium equation JO - Comptes Rendus. Mathématique PY - 2011 SP - 641 EP - 645 VL - 349 IS - 11-12 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2011.06.003/ DO - 10.1016/j.crma.2011.06.003 LA - en ID - CRMATH_2011__349_11-12_641_0 ER -
%0 Journal Article %A Biler, Piotr %A Imbert, Cyril %A Karch, Grzegorz %T Barenblatt profiles for a nonlocal porous medium equation %J Comptes Rendus. Mathématique %D 2011 %P 641-645 %V 349 %N 11-12 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2011.06.003/ %R 10.1016/j.crma.2011.06.003 %G en %F CRMATH_2011__349_11-12_641_0
Biler, Piotr; Imbert, Cyril; Karch, Grzegorz. Barenblatt profiles for a nonlocal porous medium equation. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 641-645. doi: 10.1016/j.crma.2011.06.003
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