Barenblatt profiles for a nonlocal porous media equation

Piotr Biler, Cyril Imbert, Grzegorz Karch

Published 2010-01-06, updated 2011-06-06Version 2

We study a generalization of the porous medium equation involving nonlocal terms. More precisely, explicit self-similar solutions with compact support generalizing the Barenblatt solutions are constructed. We also present a formal argument to get the $L^p$ decay of weak solutions of the corresponding Cauchy problem.