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.
Citation
C. Landim. "Hydrodynamical Equation for Attractive Particle Systems on $\mathbb{Z}^d$." Ann. Probab. 19 (4) 1537 - 1558, October, 1991. https://doi.org/10.1214/aop/1176990222
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