Hydrodynamics of a Driven Lattice Gas with Open Boundaries: the Asymmetric Simple Exclusion

#### O. Benois, R. Esposito, R. Marra, M. Mourragui

2004, v.10, Issue 1

ABSTRACT

We consider the asymmetric simple exclusion process in $d\ge 3$ with
open boundaries. The particle reservoirs of constant densities are
modeled by birth and death processes at the boundary. We prove that,
if the initial density and the densities of the boundary reservoirs
differ for order of $\ve$ from $1/2$, the empirical density field,
rescaled as $\ve^{-1}$, converges to the solution of the
initial-boundary value problem for the viscous Burgers equation in a
finite domain with given density on the boundary.

Keywords: interacting particle systems, open systems, hydrodynamic limit