Abstract
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 nonconvex 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.
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Bolley, F., Gentil, I. & Guillin, A. Uniform Convergence to Equilibrium for Granular Media. Arch Rational Mech Anal 208, 429–445 (2013). https://doi.org/10.1007/s00205-012-0599-z
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DOI: https://doi.org/10.1007/s00205-012-0599-z