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Barenblatt profiles for a nonlocal porous media equation

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Date
2011
Link to item file
http://hal.archives-ouvertes.fr/hal-00444392/fr/
Dewey
Analyse
Sujet
Riesz potential; fractional Laplacian; porous medium equation; Self-similar solutions
Journal issue
Comptes rendus mathématique
Volume
349
Number
11-12
Publication date
2011
Article pages
641-645
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.crma.2011.06.003
URI
https://basepub.dauphine.fr/handle/123456789/6502
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Karch, Grzegorz
Imbert, Cyril
Biler, Piotr
Type
Article accepté pour publication ou publié
Abstract (EN)
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 $L^p$ decay of weak solutions of the corresponding Cauchy problem.

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