We establish hydrodynamic limits for a class of attractive, reversible particle systems with an infinite range of interaction. The limiting nonlinear diffusion equations have diffusion coefficients which are functions of the local density, and which have a singularity at a critical value of the density. On open driven systems, these singular diffusion limits explain the observed nontrivial scaling behavior known as self-organized criticality.
Publié le : 1993-07-14
Classification:
Hydrodynamic limit,
singular diffusion,
fast diffusion,
self-organized criticality,
60K35,
82C20
@article{1176989122,
author = {Carlson, J. M. and Grannan, E. R. and Swindle, G. H. and Tour, J.},
title = {Singular Diffusion Limits of a Class of Reversible Self-Organizing Particle Systems},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 1372-1393},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989122}
}
Carlson, J. M.; Grannan, E. R.; Swindle, G. H.; Tour, J. Singular Diffusion Limits of a Class of Reversible Self-Organizing Particle Systems. Ann. Probab., Tome 21 (1993) no. 4, pp. 1372-1393. http://gdmltest.u-ga.fr/item/1176989122/