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Nonlocal porous medium equation: Barenblatt profiles and other weak solutions

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00795420
Contributor : Cyril Imbert <>
Submitted on : Thursday, February 28, 2013 - 10:17:33 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
Document(s) archivé(s) le : Wednesday, May 29, 2013 - 4:00:39 AM

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Piotr Biler, Cyril Imbert, Grzegorz Karch. Nonlocal porous medium equation: Barenblatt profiles and other weak solutions. Archive for Rational Mechanics and Analysis, Springer Verlag, 2015, 215 (2), pp.497-529. ⟨10.1007/s00205-014-0786-1⟩. ⟨hal-00795420⟩

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