{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:55:58Z","timestamp":1787320558113,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We prove that the beam equation with clamped ends is locally controllable in a $H^{5+\\epsilon} \\times H^{3+\\epsilon} ((0,1),\\mathbb{R})$-neighborhood of a particular trajectory of the free system, with $\\epsilon&gt;0$ and with control functions in $H^{1}_{0}((0,T),\\mathbb{R})$. Ball,. Marsden, and Slemrod already proved that this equation is not controllable in $H^{2}_{0} \\times L^{2}((0,1),\\mathbb{R})$ with control functions in $L^{r}_{\\text{loc}}(\\mathbb{R},\\mathbb{R})$, $r&gt;1$. This article justifies that their negative result is due to a choice of functional spaces which does not allow controllability. Our proof uses moment theory and the Nash\u2013Moser theorem.<\/jats:p>","DOI":"10.1137\/050642034","type":"journal-article","created":{"date-parts":[[2008,3,21]],"date-time":"2008-03-21T18:06:56Z","timestamp":1206122816000},"page":"1219-1273","source":"Crossref","is-referenced-by-count":23,"title":["Local Controllability of a One-Dimensional Beam Equation"],"prefix":"10.1137","volume":"47","author":[{"given":"Karine","family":"Beauchard","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,3,21]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0320042"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2007047"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2005.02.005"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2005.03.021"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211563"},{"key":"R6","first-page":"271","volume":"317","author":"Coron J.-M.","year":"1993","journal-title":"C. 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