Barenblatt profiles for a nonlocal porous media equation

Abstract

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.Comment: Note \`a para\^itre au Comptes-Rendus Math\'ematiqu