Fractal 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. In particular, the $L^p$ decay of solutions of the Cauchy problem is proved. Explicit self-similar solutions with compact support generalizing the KZB (or Barenblatt) solutions are constructed in the case corresponding to transport equation with a nonlocal velocity.

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. Fractal porous media equation. 2010. ⟨hal-00444392v1⟩