Piotr Biler, Cyril Imbert, Grzegorz Karch
Published 2013-02-28Version 1
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.
A note about existence for a class of viscous fluid problems
A priori bounds for weak solutions to elliptic equations with nonstandard growth
Long-time asymptotics for nonlocal porous medium equation with absorption or convection
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