Discretizing Wasserstein gradient flows: simple examples with surprising properties
speaker: Daniel Matthes (Technische Universität München)abstract: Four evolution equations are considered: the linear heat equation, the quadratic porous medium equation, the fourth order DLSS equation and a non-local QDD model. These PDEs have in common that in addition to their gradient flow structure in L2-Wasserstein, they have further substantial analytical properties that facilitate the analysis, like contractivity in the Hellinger metric or in a novel variant of the martingale OT distance. For each of the PDEs, we propose a spatial discretization that is simple but provides approximative solutions which are global, positive, and preserve an (at least in the case of DLSS: surprisingly large) number of the aforementioned structural properties. The latter are key e.g. in the convergence analysis, or for proving long-time asymptotics directly on the discrete level. This is joint work with Giuseppe Savare, Andre Schlichting, and Eva-Maria Rott.
timetable:
Tue 3 Dec, 12:00 - 12:45, Aula Dini
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