Date: Oct 28, 2014, time: 16:50
Abstract. In this work we present a macroscopic crowd motion model under hard con-
gestion eﬀects with a non-degenerate diﬀusion in the movement. This could be seen as
a second order version of the models studied by B. Maury, A. Roudneﬀ-Chupin and F.
Santambrogio (2010). In our model we consider general velocity ﬁelds (not ecessarily
gradients, and with minimal regularity assumptions) and study splitting-type schemes to show that the problem has a solution. The scheme is constructed with the help of the Fokker-Planck equation and the projection operator in the Wasserstein space. Compactness estimates to prove convergence are obtained by standard comparisons between metric derivative in Wand dissipation of the entropy, together with the analysis of the 2projection operator. This operator decreases both the entropy and the total variation.
This also allows to provide Lipschitz in time estimates for the curves of densities of the population w.r.t. the 1-Wasserstein distance. This is a joint work with F. Santambrogio