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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Maxime Laborde

12 On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows

Maxime Laborde, CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, FRANCE, laborde@ceremade.dauphine.fr

Abstract: This chapter presents existence and uniqueness results for a class of parabolic systems with nonlinear diffusion and nonlocal interaction. These systems can be viewed as regular perturbations of Wasserstein gradient flows. Here, we extend results known in the periodic case [1] to the whole space and on a smooth bounded domain. Existence is obtained using a semi-implicit Jordan–Kinderlehrer–Otto scheme and uniqueness follows from a displacement convexity argument.

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