Nonlinear porous medium flow with fractional potential pressure

Abstract

We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove existence of a weak and bounded solution that propagates with finite speed, a property that is nor shared by other fractional diffusion models.

32 pages, Latex

References in corpus (1)

• Nonlinear diffusion of dislocation density and self-similar solutions

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