The porous medium equation on manifolds with conical singularities | Prof. Elmar Schrohe (Universität Hannover)
The porous medium equation is the quasilinear diffusion equation
It describes - for example - the flow of a gas in a porous medium.
Here u is the density of the gas, m is positive, and f is a forcing term.
In the absence of exterior influence, f=0. For m=1 we obtain the usual heat
We study this equation on a manifold with conical singularities.
A few questions I would like to address in this talk:
- Why study such an equation in a singular situation?
- Do solutions exist? What methods can one apply to find them?
- Does the solution exhibit special features that can be traced back to the singular geometry?
(Joint work with Nikolaos Roidos and Jörg Seiler)
Einladung von Prof. Pohl und Dr. Doll