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Uniform convergence to equilibrium for granular media

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BGG-granularmedia.pdf (170.0Kb)
Date
2013
Link to item file
http://hal.archives-ouvertes.fr/hal-00688780
Dewey
Analyse
Sujet
rate of convergence; Wasserstein distance; Diffusion equations
Journal issue
Archive for Rational Mechanics and Analysis
Volume
208
Number
2
Publication date
2013
Article pages
429-445
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00205-012-0599-z
URI
https://basepub.dauphine.fr/handle/123456789/9012
Collections
  • CEREMADE : Publications
Metadata
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Author
Guillin, Arnaud
Gentil, Ivan
Bolley, François
Type
Article accepté pour publication ou publié
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.

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