{"paper":{"title":"Exact controllability and stability of the Sixth Order Boussinesq equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bing-Yu Zhang, Min Chen, Shenghao Li","submitted_at":"2018-11-14T18:23:34Z","abstract_excerpt":"The article studies the exact controllability and the stability of the sixth order Boussinesq equation\n  \\[ u_{tt}-u_{xx}+\\beta u_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=f, \\quad \\beta=\\pm1, \\]\n  on the interval $S:=[0,2\\pi]$ with periodic boundary conditions.\n  It is shown that the system is locally exactly controllable in the classic Sobolev space, $H^{s+3}(S)\\times H^s(S)$ for $s\\geq 0$, for \"small\" initial and terminal states. It is also shown that if $f$ is assigned as an internal linear feedback, the solution of the system is uniformly exponential decay to a constant state in $H^{s+3}(S)\\times H^s("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05943","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"}