{"paper":{"title":"Optimal time for the controllability of linear hyperbolic systems in one dimensional space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Hoai-Minh Nguyen, Jean-Michel Coron","submitted_at":"2018-05-03T07:36:52Z","abstract_excerpt":"We are concerned about the controllability of a general linear hyperbolic system of the form $\\partial_t w (t, x) = \\Sigma(x) \\partial_x w (t, x) + \\gamma C(x) w(t, x) $ ($\\gamma \\in \\mR$) in one space dimension using boundary controls on one side. More precisely, we establish the optimal time for the null and exact controllability of the hyperbolic system for generic $\\gamma$. We also present examples which yield that the generic requirement is necessary. In the case of constant $\\Sigma$ and of two positive directions, we prove that the null-controllability is attained for any time greater th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01144","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"}