Uniform convergence to equilibrium for granular media

François Bolley (1) , Ivan Gentil (2) , Arnaud Guillin (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 ICJ - Institut Camille Jordan
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

We study the long time asymptotics of a nonlinear, nonlocal equation used in the modelling of granular media. We prove a uniform exponential convergence to equilibrium for degenerately convex and non convex interaction or confinement potentials, improving in particular results by J. A. Carrillo, R. J. McCann and C. Villani. The method is based on studying the dissipation of the Wasserstein distance between a solution and the steady state.

Mots clés: Diffusion equations; Wasserstein distance; rate of convergence

Domaines: Equations aux dérivées partielles [math.AP]

François Bolley, Ivan Gentil, Arnaud Guillin. Uniform convergence to equilibrium for granular media. Archive for Rational Mechanics and Analysis, 2013, 208 (2), pp.429-445. ⟨hal-00688780⟩