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Uniform convergence to equilibrium for granular media

Guillin, Arnaud; Gentil, Ivan; Bolley, François (2013), Uniform convergence to equilibrium for granular media, Archive for Rational Mechanics and Analysis, 208, 2, p. 429-445. http://dx.doi.org/10.1007/s00205-012-0599-z

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Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00688780
Date
2013
Journal name
Archive for Rational Mechanics and Analysis
Volume
208
Number
2
Publisher
Springer
Pages
429-445
Publication identifier
Metadata
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Author(s)
Guillin, Arnaud
Gentil, Ivan
Bolley, François
Abstract (EN)
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.
Subjects / Keywords
rate of convergence; Wasserstein distance; Diffusion equations