Title: The Fractional Porous Medium Equation on Manifolds with Conic Singularities

Abstract: Due to the need to model long range diffusive interaction, during the last decade there has been a growing interest in considering diffusion equations involving non-local operators, e.g. the fractional powers of differential operators. In this talk, I will report some recent work with Nikolaos Roidos on the fractional porous medium equation on manifolds with cone-like singularities. I will show that most of the properties of the usual (local) porous medium equation, like existence, uniqueness of weak solution, comparison principle, conservation of mass, are inherited by the non-local version.