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:
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Piotr Biler 1; Cyril Imbert 2; Grzegorz Karch 1
@article{CRMATH_2011__349_11-12_641_0,
author = {Piotr Biler and Cyril Imbert and Grzegorz Karch},
title = {Barenblatt profiles for a nonlocal porous medium equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {641--645},
publisher = {Elsevier},
volume = {349},
number = {11-12},
year = {2011},
doi = {10.1016/j.crma.2011.06.003},
language = {en},
}
TY - JOUR AU - Piotr Biler AU - Cyril Imbert AU - Grzegorz Karch 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 DO - 10.1016/j.crma.2011.06.003 LA - en ID - CRMATH_2011__349_11-12_641_0 ER -
Piotr Biler; Cyril Imbert; Grzegorz Karch. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.003/
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