{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:49:37Z","timestamp":1787323777098,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"name":"LIA COPDESC"},{"name":"University Italo Francese"},{"name":"Istituto Nazionale di Alta Matematica"},{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["CUP E83C18000100006"],"award-info":[{"award-number":["CUP E83C18000100006"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We consider the linear degenerate wave equation, on the interval [Formula: see text] [Formula: see text], with bilinear control [Formula: see text] and Neumann boundary conditions. We study the controllability of this nonlinear control system, locally around a constant reference trajectory, the \u201cground state.\u201d Under some classical and generic assumptions on [Formula: see text], we prove that there exists a threshold value for time, [Formula: see text], such that the reachable set is a neighborhood of the ground state. If [Formula: see text] it is contained in a [Formula: see text]-submanifold of infinite codimension. Finally, it [Formula: see text] and [Formula: see text] it is a [Formula: see text]-submanifold of codimension 1 and if [Formula: see text] the reachable set is a neighborhood of the ground state. The case [Formula: see text] remains open. This extends to the degenerate case the work [K. Beauchard, J. Differential Equations, 250 (2011), pp. 2064\u20132098] and adapts to bilinear controls the work [F. Alabau-Boussouira, P. Cannarsa, and G. Leugering, SIAM J. Control Optim., 55 (2017), pp. 2052\u20132087]. Our proofs are based on a careful analysis of the spectral problem and on Ingham type results, which are extensions of Kadec\u2019s [Formula: see text] theorem.<\/jats:p>","DOI":"10.1137\/22m148745x","type":"journal-article","created":{"date-parts":[[2023,11,2]],"date-time":"2023-11-02T04:01:03Z","timestamp":1698897663000},"page":"6517-6553","source":"Crossref","is-referenced-by-count":4,"title":["Bilinear Control of a Degenerate Hyperbolic Equation"],"prefix":"10.1137","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2576-2004","authenticated-orcid":true,"given":"Piermarco","family":"Cannarsa","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Roma Tor Vergata, 00133, Roma, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick","family":"Martinez","sequence":"additional","affiliation":[{"name":"Institut de Math\u00e9matiques de Toulouse; UMR, 5219, Universit\u00e9 de Toulouse; CNRS UPS IMT F-31062 Toulouse Cedex 9, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3355-7879","authenticated-orcid":true,"given":"Cristina","family":"Urbani","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Roma Tor Vergata, 00133, Roma, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,11,2]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1020538"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-020-00611-z"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-022-00770-7"},{"key":"ref4","volume-title":"Families of Exponentials","author":"Avdonin S. 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