{"paper":{"title":"Control From an Interior Hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Jeffrey Galkowski, Matthieu L\\'eautaud","submitted_at":"2017-11-10T17:56:15Z","abstract_excerpt":"We consider a compact Riemannian manifold $M$ (possibly with boundary) and $\\Sigma \\subset M\\setminus \\partial M$ an interior hypersurface (possibly with boundary). We study observation and control from $\\Sigma$ for both the wave and heat equations. For the wave equation, we prove controllability from $\\Sigma$ in time $T$ under the assumption $(\\mathcal{T}GCC)$ that all generalized bicharacteristics intersect $\\Sigma$ transversally in the time interval $(0,T)$. For the heat equation we prove unconditional controllability from $\\Sigma$. As a result, we obtain uniform lower bounds for the Cauchy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03939","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"}