{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:39:40Z","timestamp":1787323180208,"version":"build-2736575974"},"reference-count":24,"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":[[2007,1]]},"abstract":"<jats:p>We consider the boundary controllability problem for a nonlinear Korteweg\u2013de Vries equation with the Dirichlet boundary condition. We study this problem for a spatial domain with a critical length for which the linearized control system is not controllable. In order to deal with the nonlinearity, we use a power series expansion of second order. We prove that the nonlinear term gives the local exact controllability around the origin provided that the time of control is large enough.<\/jats:p>","DOI":"10.1137\/06065369x","type":"journal-article","created":{"date-parts":[[2007,8,31]],"date-time":"2007-08-31T18:37:13Z","timestamp":1188585433000},"page":"877-899","source":"Crossref","is-referenced-by-count":77,"title":["Exact Controllability of a Nonlinear Korteweg\u2013de Vries Equation on a Critical Spatial Domain"],"prefix":"10.1137","volume":"46","author":[{"given":"Eduardo","family":"Cerpa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,6,12]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2005.02.005"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2005.03.021"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211563"},{"key":"R4","first-page":"155","volume":"75","author":"Coron J.-M.","year":"1996","journal-title":"J. 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Cr\u00e9peau,\n                      Contr\u00f4labilit\u00e9 exacte d'\u00e9quations dispersives issues de la m\u00e9canique\n                      , Ph.D. thesis, Laboratoire de Math\u00e9matiques, Universit\u00e9 Paris-Sud, Paris, 2002."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996301609"},{"key":"R13","first-page":"841","volume":"312","author":"Komornik V.","year":"1991","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1080\/14786449508620739"},{"key":"R15","unstructured":"J. L. Lions,\n                      Contr\u00f4labilit\u00e9 exacte, perurbations et stabilization de syst\u00e8mes distribu\u00e9s\n                      , Masson, Paris, 1988."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"G. Perla Menzala, C. F. Vasconcellos, and E. Zuazua,\n                      Stabilization of the Korteweg-de Vries equation with localized damping\n                      , Quart. Appl. 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