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.

Note à paraître au Comptes-Rendus Mathématique

References in corpus (1)

• Existence of solutions for a higher order non-local equation appearing in crack dynamics

Cited by in corpus (3)

• Entropy Solution Theory for Fractional Degenerate Convection-Diffusion Equations
• Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
• Fractional calculus for power functions