Optimal Transportation and Applications

EDP convergence and optimal transport

speaker: Alexander Mielke (WIAS Berlin and Humboldt University Berlin)

abstract: We discuss the new notion of EDP convergence for gradient systems. This convergence is based on De Giorgi's energy-dissipation principle (EDP) and has the property we can study coarse-graining limits for families $$(Q,\mathcal E_\varepsilon, \mathcal R_\varepsilon)$$ of gradient systems. While the energies $$\mathcal E_\varepsilon$$ simply converge in the sense of De Giorgi's Gamma convergence, the emergence of the effective dissipation potential $$\mathcal R_\mathrm{eff}$$ is more involved.

We will show that starting from Wasserstein gradient flows, where the dissipation potential is quadratic, we can obtain non-quadratic effective dissipation potential. We will exemplify this (i) for the membrane limit of a thin layer of low mobility and (ii) for the limit passage from diffusion to reaction.

References: WIAS preprints 2148 and 2459.

timetable:
Tue 13 Nov, 14:30 - 15:20, Aula Dini
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