Fractal porous medium equation
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
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00444392/fr/
Conference titleEmerging Topics in Dynamical Systems and Partial Differential Equations (DSPDES 2010)
MetadataShow full item record
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 / KeywordsSelf-similar solutions; $L^p$-estimates; porous medium equation; Riesz potential; fractional Laplacian
Showing items related by title and author.
Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater's models Karch, Grzegorz; Biler, Piotr; Dolbeault, Jean; Esteban, Maria J. (2001) Article accepté pour publication ou publié