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The nonlocal porous medium equation: Barenblatt profiles and other weak solutions

Karch, Grzegorz; Imbert, Cyril; Biler, Piotr (2015), The nonlocal porous medium equation: Barenblatt profiles and other weak solutions, Archive for Rational Mechanics and Analysis, 215, 2, p. 497-529. http://dx.doi.org/10.1007/s00205-014-0786-1

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00795420
Date
2015
Journal name
Archive for Rational Mechanics and Analysis
Volume
215
Number
2
Publisher
Springer
Pages
497-529
Publication identifier
Metadata
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Author(s)
Karch, Grzegorz
Imbert, Cyril cc
Biler, Piotr
Abstract (EN)
A degenerate nonlinear nonlocal evolution equation is considered; it can be understood as a porous medium equation whose pressure law is nonlinear and nonlocal. We show the existence of sign changing weak solutions to the corresponding Cauchy problem. Moreover, we construct explicit compactly supported self-similar solutions which generalize Barenblatt profiles --- the well-known solutions of the classical porous medium equation.
Subjects / Keywords
self-similar solutions; hypercontractivity; nonlocal equation; porous medium equation