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

2006/12/04 by Christophe Bahadoran, Bahadoran, Christophe
Mathematics · #35L50 #35L65 #35L67 #60K35 #82C22 #82C26 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35L50 #msc:35L65 #msc:35L67 #msc:60K35 #msc:82C22 #msc:82C26

paper · pdf · doi:10.48550/arxiv.math/0612094

arxiv created 2011/09/02 · arxiv updated 2011/09/05

Abstract

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 Nédélec. For the hydrostatic limit between parallel hyperplanes, we prove a multidimensional version of the phase diagram conjectured in \citeps, and show that it is robust with respect to perturbations of the boundaries.

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