Hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundaries

Christophe Bahadoran

Published 2006-12-04, updated 2011-09-02Version 3

We consider attractive particle systems in $\Z^d$ with product invariant measures. We prove that when particles are restricted to a subset of $\Z^d$, with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the unique entropy solution of a conservation law, with boundary conditions in the sense of Bardos, Leroux and N\'ed\'elec. For the hydrostatic limit between parallel hyperplanes, we prove a multidimensional version of the phase diagram conjectured in \cite{ps}, and show that it is robust with respect to perturbations of the boundaries.