{"paper":{"title":"Observability properties of the homogeneous wave equation on a closed manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA","math.OC"],"primary_cat":"math.AP","authors_text":"Emmanuel Humbert (LMPT), Emmanuel Tr\\'elat (CaGE, LJLL), Yannick Privat (LJLL)","submitted_at":"2016-07-06T09:31:58Z","abstract_excerpt":"We consider the wave equation on a closed Riemannian manifold. We observe the restriction of the solutions to a measurable subset $\\omega$ along a time interval $[0, T]$ with $T>0$. It is well known  that, if $\\omega$ is open and if the pair $(\\omega,T)$ satisfies the Geometric Control Condition then an observability inequality is satisfied, comparing the total energy of solutions to their energy localized in $\\omega \\times (0, T)$. The observability constant $C\\_T({\\omega})$ is then defined as the infimum over the set of all nontrivial solutions of the wave equation of the ratio of localized "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01535","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"}