## The Annals of Probability

### Hydrodynamical Equation for Attractive Particle Systems on $\mathbb{Z}^d$

C. Landim

#### Abstract

We prove conservation of local equilibrium, away from the shock, for some attractive asymmetric particle systems on $\mathbb{Z}^d$. The method applies to a class of particle processes which includes zero-range and simple exclusion processes. The main point in the proof is to exploit attractiveness. The hydrodynamic equation obtained is a first-order nonlinear partial differential equation which presents shock waves.

#### Article information

Source
Ann. Probab., Volume 19, Number 4 (1991), 1537-1558.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176990222

Digital Object Identifier
doi:10.1214/aop/1176990222

Mathematical Reviews number (MathSciNet)
MR1127714

Zentralblatt MATH identifier
0798.60084

JSTOR
Landim, C. Hydrodynamical Equation for Attractive Particle Systems on $\mathbb{Z}^d$. Ann. Probab. 19 (1991), no. 4, 1537--1558. doi:10.1214/aop/1176990222. https://projecteuclid.org/euclid.aop/1176990222