{"paper":{"title":"Analysis of the controllability from the exterior of strong damping nonlocal wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahamadi Warma, Sebastian Zamorano","submitted_at":"2018-10-18T13:55:13Z","abstract_excerpt":"We make a complete analysis of the controllability properties from the exterior of the (possible) strong damping wave equation with the fractional Laplace operator subject to the nonhomogeneous Dirichlet type exterior condition. In the first part, we show that if $0<s<1$, $\\Omega\\subset\\RR^N$ ($N\\ge 1$) is a bounded Lipschitz domain and the parameter $\\delta> 0$, then there is no control function $g$ such that the following system \\begin{equation*} \\begin{cases} u_{tt} + (-\\Delta)^{s} u + \\delta(-\\Delta)^{s} u_{t}=0 & \\mbox{ in }\\; \\Omega\\times(0,T),\\\\ u=g\\chi_{\\mathcal O\\times (0,T)} &\\mbox{ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08060","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"}