Barenblatt profiles for a nonlocal porous media equation

Piotr Biler (1) , Cyril Imbert (2) , Grzegorz Karch (1)

1 Instytut Matematyczny
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Self-similar solutions; $L^p$-estimates; porous medium equation; Riesz potential; fractional Laplacian

Domaines: Equations aux dérivées partielles [math.AP]

Piotr Biler, Cyril Imbert, Grzegorz Karch. Barenblatt profiles for a nonlocal porous media equation. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2011, 349, pp.641-645. ⟨10.1016/j.crma.2011.06.003⟩. ⟨hal-00444392v2⟩