{"paper":{"title":"A class of quasi-linear Allen-Cahn type equations with dynamic boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gianni Gilardi, Ken Shirakawa, Pierluigi Colli, Ryota Nakayashiki","submitted_at":"2016-10-27T10:07:39Z","abstract_excerpt":"In this paper, we consider a class of coupled systems of PDEs, denoted by (ACE)$_{\\varepsilon}$ for $ \\varepsilon \\geq 0 $. For each $ \\varepsilon \\geq 0 $, the system (ACE)$_{\\varepsilon}$ consists of an Allen-Cahn type equation in a bounded spacial domain $ \\Omega $, and another Allen-Cahn type equation on the smooth boundary $ \\Gamma := \\partial \\Omega $, and besides, these coupled equations are transmitted via the dynamic boundary conditions. In particular, the equation in $ \\Omega $ is derived from the non-smooth energy proposed by Visintin in his monography \"Models of phase transitions\":"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08687","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"}