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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00795420
Journal nameArchive for Rational Mechanics and Analysis
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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 / Keywordsself-similar solutions; hypercontractivity; nonlocal equation; porous medium equation
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