{"paper":{"title":"Existence and energy estimates of weak solutions for nonlocal Cahn--Hilliard equations on unbounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shunsuke Kurima","submitted_at":"2018-06-17T10:47:21Z","abstract_excerpt":"This paper considers the initial-boundary value problem for the nonlocal Cahn--Hilliard equation $$ \\partial_t\\varphi + (-\\Delta+1)(a(\\cdot)\\varphi -J\\ast\\varphi + G'(\\varphi)) = 0 \\quad \\mbox{in}\\ \\Omega\\times(0, T) $$ in an unbounded domain $\\Omega \\subset \\mathbb{R}^N$ with smooth bounded boundary, where $N\\in\\mathbb{N}$, $T>0$, and $a(\\cdot), J, G$ are given functions. In the case that $\\Omega$ is a bounded domain and $-\\Delta+1$ is replaced with $-\\Delta$, this problem has been studied by using a Faedo--Galerkin approximation scheme considering the compactness of the Neumann operator $-\\D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06361","kind":"arxiv","version":1},"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"}