Difusión no lineal en Madrid
Seminario conjunto de las universidades: UAM, UC3M, UCM, UPM y URJC
Resumen. The effect of geometry on diffusion (and vice versa) is a well-known topic in PDEs, recently its interest has extended to nonlinear flows. We will present the theory of porous medium flows on manifolds with negative curvature and we will get a precise description of the fundamental solution in the Hyperbolic Space, which is almost explicit but strongly departs from the Euclidean counterpart.
This applies to general solutions. A key tool in the fine analysis is a partial equivalence with a family of weighted porous medium equations posed on Euclidean space.
We end up by extending the analysis to other negatively curved manifolds (this last part is joint work with G. Grillo and M. Muratori).
Organizado por los proyectos: MTM2014-52240-P y MTM2014-53037-P
Comité organizador: Matteo Bonforte, Mar González, Arturo de Pablo y Fernando Quirós