Barenblatt profiles for a nonlocal porous media equation

Details Barenblatt profiles for a nonlocal porous media equation Barenblatt profiles for a nonlocal porous media equation

2010-01-06

arxiv.org/abs/1001.0910v2

Mathematics

Analysis of PDEs

Note \`a para\^itre au Comptes-Rendus Math\'ematique

Scientific paper

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.

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