{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T16:04:13Z","timestamp":1769443453040,"version":"3.49.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,10,15]],"date-time":"2022-10-15T00:00:00Z","timestamp":1665792000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,10,15]],"date-time":"2022-10-15T00:00:00Z","timestamp":1665792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Control Signals Syst."],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s00498-022-00331-4","type":"journal-article","created":{"date-parts":[[2022,10,15]],"date-time":"2022-10-15T18:02:36Z","timestamp":1665856956000},"page":"77-123","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Exact boundary controllability of 1D semilinear wave equations through a constructive approach"],"prefix":"10.1007","volume":"35","author":[{"given":"Kuntal","family":"Bhandari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00e9r\u00f4me","family":"Lemoine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arnaud","family":"M\u00fcnch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,15]]},"reference":[{"issue":"5","key":"331_CR1","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1080\/03605302.2013.771659","volume":"38","author":"L Baudouin","year":"2013","unstructured":"Baudouin L, De Buhan M, Ervedoza S (2013) Global Carleman estimates for waves and applications. Commun Partial Differ Equ 38(5):823\u2013859","journal-title":"Commun Partial Differ Equ"},{"key":"331_CR2","doi-asserted-by":"crossref","unstructured":"Burman E, Feizmohammadi A, M\u00fcnch A, Oksanen L (2021) Space time finite element methods for control problems subject to the wave equation. Preprint hal-03346617","DOI":"10.1051\/m2an\/2020062"},{"issue":"5","key":"331_CR3","doi-asserted-by":"publisher","first-page":"784","DOI":"10.1002\/nme.1620170510","volume":"17","author":"M Bernadou","year":"1981","unstructured":"Bernadou M, Hassan K (1981) Basis functions for general Hsieh\u2013Clough\u2013Tocher triangles, complete or reduced. Intern J Numer Methods Eng 17(5):784\u2013789","journal-title":"Intern J Numer Methods Eng"},{"key":"331_CR4","unstructured":"Bottois A, Lemoine J, M\u00fcnch A (2021) Constructive exact control of semilinear multi-dimensional wave equations by a least-squares approach. Preprint hal-03112309"},{"issue":"5","key":"331_CR5","doi-asserted-by":"publisher","first-page":"1024","DOI":"10.1137\/0330055","volume":"30","author":"C Bardos","year":"1992","unstructured":"Bardos C, Lebeau G, Rauch J (1992) Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J Control Optim 30(5):1024\u20131065","journal-title":"SIAM J Control Optim"},{"key":"331_CR6","volume-title":"Carleman estimates and applications to inverse problems for hyperbolic systems. Springer Monographs in Mathematics","author":"M Bellassoued","year":"2017","unstructured":"Bellassoued M, Yamamoto M (2017) Carleman estimates and applications to inverse problems for hyperbolic systems. Springer Monographs in Mathematics. Springer, Tokyo"},{"key":"331_CR7","doi-asserted-by":"crossref","unstructured":"Calvalcanti M, Cavalcanti V, Carole R, Rosier L (2021) Numerical control of a semilinear wave equation on an interval. Preprint, hal-03369560","DOI":"10.1007\/978-3-030-94766-8_4"},{"issue":"4","key":"331_CR8","doi-asserted-by":"publisher","first-page":"1076","DOI":"10.1051\/cocv\/2013046","volume":"19","author":"N C\u00eendea","year":"2013","unstructured":"C\u00eendea N, Fern\u00e1ndez-Cara E, M\u00fcnch A (2013) Numerical controllability of the wave equation through primal methods and Carleman estimates. ESAIM Control Optim Calc Var 19(4):1076\u20131108","journal-title":"ESAIM Control Optim Calc Var"},{"issue":"1","key":"331_CR9","doi-asserted-by":"publisher","first-page":"21","DOI":"10.5802\/afst.543","volume":"2","author":"T Cazenave","year":"1980","unstructured":"Cazenave T, Haraux A (1980) \u00c9quations d\u2019\u00e9volution avec non lin\u00e9arit\u00e9 logarithmique. Ann Fac Sci Toulouse Math (5) 2(1):21\u201351","journal-title":"Ann Fac Sci Toulouse Math (5)"},{"issue":"1","key":"331_CR10","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1137\/0314002","volume":"14","author":"WC Chewning","year":"1976","unstructured":"Chewning WC (1976) Controllability of the nonlinear wave equation in several space variables. SIAM J Control Optim 14(1):19\u201325","journal-title":"SIAM J Control Optim"},{"key":"331_CR11","unstructured":"Ciarlet PG (2002) The finite element method for elliptic problems, volume\u00a040 of classics in applied mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA. Reprint of the 1978 original [North-Holland, Amsterdam; MR0520174 (58 #25001)]"},{"issue":"3","key":"331_CR12","doi-asserted-by":"publisher","first-page":"745","DOI":"10.3934\/dcds.2002.8.747","volume":"8","author":"P Cannarsa","year":"2002","unstructured":"Cannarsa P, Komornik V, Loreti P (2002) One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms. Discrete Contin Dyn Syst 8(3):745\u2013756","journal-title":"Discrete Contin Dyn Syst"},{"issue":"3","key":"331_CR13","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s10092-014-0116-x","volume":"52","author":"N C\u00eendea","year":"2015","unstructured":"C\u00eendea N, M\u00fcnch A (2015) A mixed formulation for the direct approximation of the control of minimal $$L^2$$-norm for linear type wave equations. Calcolo 52(3):245\u2013288","journal-title":"Calcolo"},{"issue":"4","key":"331_CR14","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1142\/S0219199706002209","volume":"8","author":"J-M Coron","year":"2006","unstructured":"Coron J-M, Tr\u00e9lat E (2006) Global steady-state stabilization and controllability of 1D semilinear wave equations. Commun Contemp Math 8(4):535\u2013567","journal-title":"Commun Contemp Math"},{"issue":"2","key":"331_CR15","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1137\/070712067","volume":"48","author":"B Dehman","year":"2009","unstructured":"Dehman B, Lebeau G (2009) Analysis of the HUM control operator and exact controllability for semilinear waves in uniform time. SIAM J Control Optim 48(2):521\u2013550","journal-title":"SIAM J Control Optim"},{"issue":"4","key":"331_CR16","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1016\/S0012-9593(03)00021-1","volume":"36","author":"B Dehman","year":"2003","unstructured":"Dehman B, Lebeau G, Zuazua E (2003) Stabilization and control for the subcritical semilinear wave equation. Ann Sci \u00c9cole Norm Sup (4) 36(4):525\u2013551","journal-title":"Ann Sci \u00c9cole Norm Sup (4)"},{"key":"331_CR17","doi-asserted-by":"publisher","unstructured":"Ervedoza S, Lemoine J, M\u00fcnch A (2022) Exact controllability of semilinear heat equations through a constructive approach. Evol Equ Control Theory. https:\/\/doi.org\/10.3934\/eect.2022042","DOI":"10.3934\/eect.2022042"},{"issue":"4","key":"331_CR18","first-page":"1375","volume":"14","author":"S Ervedoza","year":"2010","unstructured":"Ervedoza S, Zuazua E (2010) A systematic method for building smooth controls for smooth data. Discrete Contin Dyn Syst Ser B 14(4):1375\u20131401","journal-title":"Discrete Contin Dyn Syst Ser B"},{"issue":"1","key":"331_CR19","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1007\/BF01698123","volume":"9","author":"HO Fattorini","year":"1975","unstructured":"Fattorini HO (1975) Local controllability of a nonlinear wave equation. Math Syst Theory 9(1):30\u201345","journal-title":"Math Syst Theory"},{"issue":"3\u20134","key":"331_CR20","first-page":"251","volume":"20","author":"F Hecht","year":"2012","unstructured":"Hecht F (2012) New development in Freefem++. J Numer Math 20(3\u20134):251\u2013265","journal-title":"J Numer Math"},{"issue":"1","key":"331_CR21","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1137\/120891174","volume":"52","author":"R Joly","year":"2014","unstructured":"Joly R, Laurent C (2014) A note on the semiglobal controllability of the semilinear wave equation. SIAM J Control Optim 52(1):439\u2013450","journal-title":"SIAM J Control Optim"},{"issue":"5","key":"331_CR22","doi-asserted-by":"publisher","first-page":"1733","DOI":"10.1137\/17M1122487","volume":"77","author":"MV Klibanov","year":"2017","unstructured":"Klibanov MV, Kolesov AE, Nguyen L, Sullivan A (2017) Globally strictly convex cost functional for a 1-D inverse medium scattering problem with experimental data. SIAM J Appl Math 77(5):1733\u20131755","journal-title":"SIAM J Appl Math"},{"key":"331_CR23","unstructured":"Lions J-L (1988) Contr\u00f4labilit\u00e9 exacte, perturbations et stabilisation de syst\u00e8mes distribu\u00e9s. Tome 1, volume\u00a08 of Recherches en Math\u00e9matiques Appliqu\u00e9es [Research in Applied Mathematics]. Masson, Paris. Contr\u00f4labilit\u00e9 exacte. [Exact controllability], With appendices by E. Zuazua, C. Bardos, G. Lebeau and J. Rauch"},{"issue":"1","key":"331_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/1030001","volume":"30","author":"J-L Lions","year":"1988","unstructured":"Lions J-L (1988) Exact controllability, stabilization and perturbations for distributed systems. SIAM Rev 30(1):1\u201368","journal-title":"SIAM Rev"},{"key":"331_CR25","unstructured":"Lagnese J, Lions J-L (1988) Modelling analysis and control of thin plates, vol 6. Recherches en Math\u00e9matiques Appliqu\u00e9es [Research in Applied Mathematics]. Masson, Paris"},{"issue":"2","key":"331_CR26","first-page":"149","volume":"65","author":"I Lasiecka","year":"1986","unstructured":"Lasiecka I, Lions J-L, Triggiani R (1986) Nonhomogeneous boundary value problems for second order hyperbolic operators. J Math Pures Appl (9) 65(2):149\u2013192","journal-title":"J Math Pures Appl (9)"},{"key":"331_CR27","doi-asserted-by":"publisher","unstructured":"Lemoine J, M\u00fcnch A (2022) Constructive exact control of semilinear 1d heat equations. Math Control Relat Fields. https:\/\/doi.org\/10.3934\/mcrf.2022001","DOI":"10.3934\/mcrf.2022001"},{"issue":"2","key":"331_CR28","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/BF01442394","volume":"23","author":"I Lasiecka","year":"1991","unstructured":"Lasiecka I, Triggiani R (1991) Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems. Appl Math Optim 23(2):109\u2013154","journal-title":"Appl Math Optim"},{"issue":"2","key":"331_CR29","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1006\/jmaa.2000.6998","volume":"250","author":"L Li","year":"2000","unstructured":"Li L, Zhang X (2000) Exact controllability for semilinear wave equations. J Math Anal Appl 250(2):589\u2013597","journal-title":"J Math Anal Appl"},{"key":"331_CR30","first-page":"78","volume":"3","author":"L Markus","year":"1965","unstructured":"Markus L (1965) Controllability of nonlinear processes. J SIAM Control Ser A 3:78\u201390","journal-title":"J SIAM Control Ser A"},{"issue":"1","key":"331_CR31","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s10444-015-9412-5","volume":"42","author":"A M\u00fcnch","year":"2016","unstructured":"M\u00fcnch A, Souza DA (2016) A mixed formulation for the direct approximation of $$L^2$$-weighted controls for the linear heat equation. Adv Comput Math 42(1):85\u2013125","journal-title":"Adv Comput Math"},{"issue":"2","key":"331_CR32","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1137\/20M1380661","volume":"60","author":"A M\u00fcnch","year":"2022","unstructured":"M\u00fcnch A, Tr\u00e9lat E (2022) Constructive exact control of semilinear 1D wave equations by a least-squares approach. SIAM J Control Optim 60(2):652\u2013673","journal-title":"SIAM J Control Optim"},{"issue":"1","key":"331_CR33","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1080\/00207179.2016.1266513","volume":"92","author":"V Natarajan","year":"2019","unstructured":"Natarajan V, Zhou H-C, Weiss G, Fridman E (2019) Exact controllability of a class of nonlinear distributed parameter systems using back-and-forth iterations. Intern J Control 92(1):145\u2013162","journal-title":"Intern J Control"},{"issue":"4","key":"331_CR34","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1137\/1020095","volume":"20","author":"DL Russell","year":"1978","unstructured":"Russell DL (1978) Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions. SIAM Rev 20(4):639\u2013739","journal-title":"SIAM Rev"},{"issue":"146","key":"331_CR35","first-page":"65","volume":"4","author":"J Simon","year":"1987","unstructured":"Simon J (1987) Compact sets in the space $$L^p(0, T;B)$$. Ann Mat Pura Appl 4(146):65\u201396","journal-title":"Ann Mat Pura Appl"},{"issue":"1997","key":"331_CR36","doi-asserted-by":"publisher","first-page":"1101","DOI":"10.1098\/rspa.2000.0553","volume":"456","author":"X Zhang","year":"2000","unstructured":"Zhang X (2000) Explicit observability estimate for the wave equation with potential and its application. R Soc Lond Proc Ser A Math Phys Eng Sci 456(1997):1101\u20131115","journal-title":"R Soc Lond Proc Ser A Math Phys Eng Sci"},{"key":"331_CR37","unstructured":"Zuazua E (1988) Contr\u00f4labilit\u00e9 exacte de syst\u00e8mes d\u2019\u00e9volution non lin\u00e9aires. C R Acad Sci Paris S\u00e9r I Math 306(3):129\u2013132"},{"key":"331_CR38","doi-asserted-by":"crossref","unstructured":"Zuazua E (1988) Exact controllability for semilinear distributed systems. In: Proceedings of the 27th IEEE conference on decision and control, pp 1265\u20131268 vol 2","DOI":"10.1109\/CDC.1988.194525"},{"issue":"1","key":"331_CR39","first-page":"1","volume":"69","author":"E Zuazua","year":"1990","unstructured":"Zuazua E (1990) Exact controllability for the semilinear wave equation. J Math Pures Appl 69(1):1\u201331","journal-title":"J Math Pures Appl"},{"key":"331_CR40","unstructured":"Zuazua E (1991) Exact boundary controllability for the semilinear wave equation. In: Nonlinear partial differential equations and their applications. Coll\u00e8ge de France Seminar, Vol. X (Paris, 1987\u20131988), volume 220 of Pitman Res. Notes Math. Ser. Longman Sci. Tech., Harlow, pp 357\u2013391"},{"issue":"1","key":"331_CR41","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/s0294-1449(16)30221-9","volume":"10","author":"E Zuazua","year":"1993","unstructured":"Zuazua E (1993) Exact controllability for semilinear wave equations in one space dimension. Ann Inst H Poincar\u00e9 Anal Non Lin\u00e9aire 10(1):109\u2013129","journal-title":"Ann Inst H Poincar\u00e9 Anal Non Lin\u00e9aire"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-022-00331-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00498-022-00331-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-022-00331-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,5]],"date-time":"2024-10-05T21:27:19Z","timestamp":1728163639000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00498-022-00331-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,15]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["331"],"URL":"https:\/\/doi.org\/10.1007\/s00498-022-00331-4","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,15]]},"assertion":[{"value":"9 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}