Archive for Rational Mechanics and Analysis

, Volume 215, Issue 2, pp 497–529 | Cite as

The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions

Article

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland
  2. 2.CNRS, UMR 8050Université Paris-Est CréteilCréteil CedexFrance

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