GRADIENT FLOW OF INTERACTION ENERGIES

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Date/heure
Date(s) - 06/03/2012
10 h 00 min - 11 h 00 min

Catégories Pas de Catégories


We consider interaction models of the form ?t? = div((?W ??)?) in (0+?)×R^n. Here, ? represents a particle density, W : R^n ? R is a potential representing their pairwise interaction. We discuss well-posedness, asymptotic properties and possible blow up in finite time, in the framework of gradient flows in probability spaces equipped with the optimal transport distance. We consider general ?-convex potentials. We also give some remarksabout the case of the newtonian potential W (x) = ? (1/2pi) log |x| in dimension 2.