{"paper":{"title":"Geometric control condition for the wave equation with a time-dependent observation domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emmanuel Tr\\'elat (IUF, Gilles Lebeau (JAD), IUF), J\\'er\\^ome Le Rousseau (LAGA, LJLL), Peppino Terpolilli (CSTJF)","submitted_at":"2016-07-06T09:09:09Z","abstract_excerpt":"We characterize the observability property (and, by duality, the  controllability and the stabilization) of the wave equation on a  Riemannian manifold $\\Omega,$ with or without boundary, where the  observation (or control) domain is time-varying. We provide a  condition ensuring observability, in terms of propagating  bicharacteristics. This condition extends the well-known geometric  control condition established for fixed observation domains.  As one of the consequences, we prove that it is always possible to  find a time-dependent observation domain of arbitrarily small  measure for which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01527","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"}