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The porous medium equation on manifolds with conical singularities

Teaser:
Startdatum: 25.06.2019 - 16:00
Enddatum: 25.06.2019 - 17:30
Adresse: MZH 6210
Organisator/Ansprechpartner: Prof. Jens Rademacher, Prof. Christine Knipping, (0421) 218-63745, (0421) 218-63721
Redner:
  • Prof. Elmar Schrohe / Universität Hannover

The porous medium equation is the quasilinear diffusion equation

u'(t)-∆(u^m(t))=f(u,t)  t>0
u(0) =u_0.

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
equation.  

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?

 

 

                                                                      Einladung von Prof. Pohl und Dr. Doll