Porous medium equation with nonlocal pressure in a bounded domain (1708.00660v1)

Published 2 Aug 2017 in math.AP

Abstract: We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplacian pressure, and the problem is posed on a bounded space domain. We prove existence of weak solutions and suitable a priori bounds and regularity estimates.

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