Structure-preserving Full Discretizations for Some Gradient Flow Equations
speaker: Daniel Matthes (Zentrum Mathematik, TU Munich)abstract: Under certain hypotheses, nonlinear Fokker-Planck equations are gradient flows for an entropy functional with respect to the Wasserstein metric. In this talk, we propose a specific discretization of these equations in space and time that is based on the variational structure: we carry out the "minimizing movement scheme" on a suitable finite-dimensional subset of the space of probability measures. We show that solutions to the resulting discrete equation inherit nice properties from the original gradient flow, like comparison principles and contractivity estimates in Wasserstein. We also prove convergence of the scheme under an "inverse" CLF condition. Finally, we discuss the extension to di usion equations of fourth order. This is a joint work with Bertram Duering and Horst Osberger.
timetable:
Tue 6 Nov, 17:15 - 17:45, Aula Dini
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