Abstract

The granular media equation is a non linear Fokker-Planck type equation, derived from the Boltzmann equation, which models the evolution of a set of particles subject to almost elastic collisions. Studying the long time behaviour of its solutions has recently raised much attention, by entropy dissipation techniques, based on its interpretation as a gradient flow in the space of probability measures, or by contraction properties in Wasserstein distance, also linked with the optimal transport problem. We will review these results, and present a new method, based on estimating the dissipation of this distance along the flow: this method enables to cover the physically relevant potentials and can hopefully be useful for other models. This is joint work with I. Gentil (Lyon) and A. Guillin (Clermont-Ferrand).