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May 2003 Convergence to equilibrium for granular media equations and their Euler schemes
Florent Malrieu
Ann. Appl. Probab. 13(2): 540-560 (May 2003). DOI: 10.1214/aoap/1050689593


We introduce a new interacting particle system to investigate the behavior of the nonlinear, nonlocal diffusive equation already studied by Benachour et al. [3, 4]. We first prove an uniform (with respect to time) propagation of chaos. Then, we show that the solution of the nonlinear PDE converges exponentially fast to equilibrium recovering a result established by an other way by Carrillo, McCann and Vilanni [7]. At last we provide explicit and Gaussian confidence intervals for the convergence of an implicit Euler scheme to the stationary distribution of the nonlinear equation.


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Florent Malrieu. "Convergence to equilibrium for granular media equations and their Euler schemes." Ann. Appl. Probab. 13 (2) 540 - 560, May 2003.


Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1031.60085
MathSciNet: MR1970276
Digital Object Identifier: 10.1214/aoap/1050689593

Primary: 65C35
Secondary: 35K55 , 65C05 , 82C22

Keywords: concentration of measure phenomenon , implicit Euler scheme , Interacting particle system , Logarithmic Sobolev inequality , nonlinear parabolic PDE , propagation of chaos

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 2 • May 2003
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