Fractal porous medium equation

Karch, Grzegorz; Imbert, Cyril; Biler, Piotr

Karch, Grzegorz; Imbert, Cyril; Biler, Piotr (2010), Fractal porous medium equation, Emerging Topics in Dynamical Systems and Partial Differential Equations (DSPDES 2010), 2010-06, Barcelone, Espagne

Type

Communication / Conférence

External document link

http://hal.archives-ouvertes.fr/hal-00444392/fr/

Date

2010

Conference title

Emerging Topics in Dynamical Systems and Partial Differential Equations (DSPDES 2010)

Conference date

2010-06

Conference city

Barcelone

Conference country

Espagne

Metadata

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Author(s)

Karch, Grzegorz
Imbert, Cyril

Biler, Piotr

Abstract (EN)

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.

Subjects / Keywords

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