Published January 1, 2015 | Version v1
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The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions

  • 1. Uniwersytet Wroclawski, Inst Matemat, PL-50384 Wroclaw, Poland
  • 2. Univ Paris Est Creteil, CNRS, UMR 8050, F-94010 Creteil, France

Description

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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