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

Nonlinear porous medium flow with fractional potential pressure