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Description

The talk aims to present two ideas, useful for proving the existence of solutions for fourth-order Cahn-Hilliard PDEs, with JKO-type schemes. The first idea is to use a scheme with weighted Wasserstein distance, if the equation has a general concave mobility m(u), instead of the usual m(u)=u which leads to the usual Wasserstein distance. These distances were introduced in *Dolbeault, Nazaret, Savaré, CalcVar 2009*. The second idea is the flow interchange lemma, which allows to compute the dissipation of an entropy along the iterations of the JKO scheme. This lemma was applied in *Lisini, Matthes, Savaré, JDE 2012*.