{"paper":{"title":"Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Flank D. M. Bezerra, Gleiciane da Silva Arag\\~ao","submitted_at":"2018-08-16T20:21:52Z","abstract_excerpt":"In this paper we are interested in the behavior of the solutions of non-autonomous damped wave equations when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter \\varepsilon goes to zero. We prove the conti- nuity of the set equilibria of these equations. Moreover, if an equilibrium solution of the limit problem is hyperbolic, then we show that the per- turbed equation has one and only one equilibrium solution nearby."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05667","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"}