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

Abstract

We consider attractive particle systems in ${\mathbb{Z}}^d$ with product invariant measures. We prove that when particles are restricted to a subset of ${\mathbb{Z}}^d$, 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 Nédélec. 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.

References in corpus (3)

• Steady-state selection in driven diffusive systems with open boundaries
• Hydrodynamics of a driven lattice gas with open boundaries: the asymmetric simple exclusion
• Exclusion Processes with Multiple Interactions

Cited by in corpus (2)

• Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process
• A quasi-potential for conservation laws with boundary conditions