Uniform Convergence to Equilibrium for Granular Media

被引：62

作者：

Bolley, Francois ^{[1
]}

Gentil, Ivan ^{[2
]}

Guillin, Arnaud ^{[3
,4
]}

机构：

[1] Univ Paris 09, UMR CNRS 7534, F-75775 Paris 16, France

[2] Univ Lyon 1, UMR CNRS 5208, Inst Camille Jordan, F-69622 Villeurbanne, France

[3] Univ Blaise Pascal, UMR CNRS 6620, Inst Univ France, F-63177 Aubiere, France

[4] Univ Blaise Pascal, UMR CNRS 6620, Math Lab, F-63177 Aubiere, France

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2013年 / 208卷 / 02期

关键词：

EQUATIONS;

D O I：

10.1007/s00205-012-0599-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：429 / 445

页数：17

共 19 条

[1]

Ambrosio L., 2006, Gradient Flows in Metric Spaces and in the Space of Probability Measures

[2] A simple proof of the Poincare inequality for a large class of probability measures including the log-concave case [J].

Bakry, Dominique ;

Barthe, Franck ;

Cattiaux, Patrick ;

Guillin, Arnaud .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2008, 13 :60-66

[3] A non-Maxwellian steady distribution for one-dimensional granular media [J].

Benedetto, D ;

Caglioti, E ;

Carrillo, JA ;

Pulvirenti, M .

JOURNAL OF STATISTICAL PHYSICS, 1998, 91 (5-6) :979-990

[4] Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations [J].

Bolley, Francois ;

Gentil, Ivan ;

Guillin, Arnaud .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (08) :2430-2457

[5] TREND TO EQUILIBRIUM AND PARTICLE APPROXIMATION FOR A WEAKLY SELFCONSISTENT VLASOV-FOKKER-PLANCK EQUATION [J].

Bolley, Francois ;

Guillin, Arnaud ;

Malrieu, Florent .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2010, 44 (05) :867-884

[6]

Calvez V, 2012, P AM MATH SOC, V140, P3515

[7]

Carrillo JA, 2007, RIV MAT UNIV PARMA, V6, P75

[8] Contractions in the 2-Wasserstein length space and thermalization of granular media [J].

Carrillo, JA ;

McCann, RJ ;

Villani, CD .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2006, 179 (02) :217-263

[9]

Carrillo JA, 2005, NEW TRENDS IN MATHEMATICAL PHYSICS, P234

[10]

Carrillo JA, 2003, REV MAT IBEROAM, V19, P971

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