Speaker
Description
Gradient flows in Hilbert spaces are conditioned by the choice of an underlying metric so that a given functional may give rise to infinitely many gradient flows. We shall investigate in this talk the possible limit behaviors of the associated evolution problems when the metric degenerates, by considering sequences of metrics which are « less and less equivalent » to the canonical one. In particular, we shall be interested in the possibility to incorporate inhibition behaviors in crowd motion models, by attributing a (infinitely) larger mass to individuals considered as prioritary according to some criteria, like simply being the closest to some common objective. We will show how this asymptotic approach transforms a crowd model on the gradient flow type into a cascade of differential inclusions. In a more exploratory part, we shall presents some attempts to apply this strategy to the setting of Wasserstein gradient flows, by having the L2 like norm on the « tangent space » degenerate.
