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.
Publié le : 2003-05-14
Classification:
Interacting particle system,
propagation of chaos,
logarithmic Sobolev inequality,
nonlinear parabolic PDE,
concentration of measure phenomenon,
implicit Euler scheme,
65C35,
35K55,
65C05,
82C22
@article{1050689593,
author = {Malrieu, Florent},
title = {Convergence to equilibrium for granular media equations and their Euler schemes},
journal = {Ann. Appl. Probab.},
volume = {13},
number = {1},
year = {2003},
pages = { 540-560},
language = {en},
url = {http://dml.mathdoc.fr/item/1050689593}
}
Malrieu, Florent. Convergence to equilibrium for granular media equations and their Euler schemes. Ann. Appl. Probab., Tome 13 (2003) no. 1, pp. 540-560. http://gdmltest.u-ga.fr/item/1050689593/