Speaker
Asuka Takatsu
(Tokyo)
Description
We discuss how concavity properties are preserved under the porous medium flows on a Riemannian manifold, clarifying the effects of diffusion nonlinearity and curvature. In particular, curvature yields an obstruction: if the sectional curvature is negative at a given point, no concavity property is preserved. However, if the curvature is non-zero, concavity properties can only be preserved if they are stronger than those associated with the diffusion nonlinearity.
This talk is based on joint work with Kazuhiro Ishige and Yoshiumi Tateoka.