{"paper":{"title":"Asymptotic behavior for a class of non autonomous non local problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antonio L. Pereira, Flank D. Bezerra, Severino H. da Silva","submitted_at":"2013-12-20T17:06:49Z","abstract_excerpt":"In this paper we consider the non local non autonomous evolution problem \\[ \\begin{cases} \\partial_t u =- u + g \\left(\\beta(t)(Ku) \\right)\\ \\ \\mbox{in}\\ \\ \\Omega,\\\\ u = 0\\ \\ \\mbox{in}\\ \\ \\mathbb{R}^N\\backslash\\Omega, \\end{cases} \\] where $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^N$, $\\beta$ denotes the functional parameter given by a continuous bounded function on $\\mathbb{R}$, and $K$ is an integral operator with symmetric kernel. We prove existence and some regularity properties of the pullback attractor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6045","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"}