{"paper":{"title":"Hydrodynamic limit for the Ginzburg-Landau $\\nabla\\phi$ interface model with a conservation law and Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Takao Nishikawa","submitted_at":"2012-11-12T12:03:06Z","abstract_excerpt":"Hydrodynamic limit for the Ginzburg-Landau $\\nabla\\phi$ interface model with a conservation law was established in [Nishikawa 2002] under the periodic boundary conditions. This paper studies the same problem on the bounded domain imposing Dirichlet boundary conditions. A nonlinear partial equation of fourth order with boundary conditions is derived as the macroscopic equation, which is related to the Wulff shape derived by [Deuschel et.al. 2000]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2586","kind":"arxiv","version":2},"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"}