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December, 2003 Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
José A. Carrillo, Robert J. McCann, Cédric Villani
Rev. Mat. Iberoamericana 19(3): 971-1018 (December, 2003).

Abstract

The long-time asymptotics of certain nonlinear, nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [BCCP98] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogeneous model of granular flow is extended and quantified by computing explicit relaxation rates. Our arguments rely on establishing generalizations of logarithmic Sobolev inequalities and mass transportation inequalities, via either the Bakry-Emery method or the abstract approach of Otto and Villani [OV00].

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José A. Carrillo. Robert J. McCann. Cédric Villani. "Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates." Rev. Mat. Iberoamericana 19 (3) 971 - 1018, December, 2003.

Information

Published: December, 2003
First available in Project Euclid: 20 February 2004

zbMATH: 1073.35127
MathSciNet: MR2053570

Subjects:
Primary: 35B40 , 35K55 , 35K65 , 35Q72

Keywords: generalized log-Sobolev inequalities , inelastic collision models , rates of convergence , Wasserstein distance

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.19 • No. 3 • December, 2003
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