„In this talk, we discuss how solutions to certain PDEs can be described within the framework of gradient flows. The most common approach involves obtaining them as limits of piecewise constant-in-time curves constructed by minimizing a problem that depends on the underlying metric and the driving functional. This may be combined with the requirement that the approximations are also piecewise constant in the spatial coordinates; in this case, the geometric structure of the tessellation becomes important. Part of this talk is dedicated to an approach that employs a hexagonal tessellation of a subset of R^2. Another topic is a time-discrete scheme that requires certain regularizations due to the possible loss of metric structure in some generalizations. Finally, we consider a method of obtaining solutions to certain PDEs using a time-continuous formulation in which the gradient flow structure is perturbed, but the underlying method remains based on a crucial variational principle.“
TopMath Talks
Im Rahmen der TopMath-Talks stellen Studierende und Promovierende des TopMath-Programms Teile ihrer Forschung vor. Sie geben einen verständlichen Einblick in ihr Interessensgebiet und ermöglichen es so Studierenden und Mitarbeitern aus unterschiedlichen Forschungsfeldern, ihre mathematische Allgemeinbildung zu erweitern. Die Talks sind öffentlich und dauern ungefähr eine Stunde mit anschließender Diskussion. Jede*r ist willkommen.