{"paper":{"title":"Hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Christophe Bahadoran","submitted_at":"2006-12-04T15:11:11Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612094","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}