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Fractal porous medium equation

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Date
2010
Link to item file
http://hal.archives-ouvertes.fr/hal-00444392/fr/
Dewey
Analyse
Sujet
Self-similar solutions; $L^p$-estimates; porous medium equation; Riesz potential; fractional Laplacian
Conference name
Emerging Topics in Dynamical Systems and Partial Differential Equations (DSPDES 2010)
Conference date
06-2010
Conference city
Barcelone
Conference country
Espagne
URI
https://basepub.dauphine.fr/handle/123456789/3875
Collections
  • CEREMADE : Publications
Metadata
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Author
Karch, Grzegorz
Imbert, Cyril
Biler, Piotr
Type
Communication / Conférence
Item number of pages
6
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.

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