Global solutions to kinetic models of granular media

par Martial Agueh (University of Victoria, BC Canada)

vendredi 21 févr. 2014, 10:30 → 11:30 Europe/Paris

203 (XLIM)

Granular materials consist of a large number of small discrete grains which interact by nearly instantaneous collisions, much like in the classical model of a gas. But the difference between collisions of granular and ideal gas particles relies in the inelasticity of the collisions between grains. In this talk, I'll present a discrete model of granular media, derive the corresponding kinetic model, then prove the global existence of weak solutions to the kinetic equation. The existence proof relies on a splitting method (separating advection in position and interaction in velocity) where the spatially homogeneous equation is interpreted as the gradient flow of a convex interaction energy (in velocity) with respect to the Wasserstein distance of the optimal transport theory.