{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:31:19Z","timestamp":1787322679108,"version":"build-2736575974"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>Various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained, but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions. In this paper, we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable. The results are obtained using new properties of symmetric operators (which are proved in this paper), compact semigroups, the Schauder fixed point theorem, and\/or the contraction mapping principle.<\/jats:p>","DOI":"10.1137\/s0363012901391688","type":"journal-article","created":{"date-parts":[[2003,11,10]],"date-time":"2003-11-10T21:00:45Z","timestamp":1068498045000},"page":"1604-1622","source":"Crossref","is-referenced-by-count":285,"title":["Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces"],"prefix":"10.1137","volume":"42","author":[{"given":"Nazim I.","family":"Mahmudov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","first-page":"53","volume":"2","author":"Ahmed N.","year":"1995","journal-title":"Nonlinear World"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02191736"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00938943"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"ViorelBarbu, GianmarioTessitore, Considerations on the controllability of stochastic linear heat equations, Lecture Notes in Pure and Appl. Math., Vol. 227, Dekker, New York, 2002, 39\u2013512003g:93008","DOI":"10.1201\/9780203910177.ch3"},{"key":"R5","volume-title":"Convexity and optimization in Banach spaces","author":"Barbu V.","year":"1986"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S036301299732184X"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1023\/A:1006510809870"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0315005"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940064"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4224-6"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511666223"},{"key":"R12","first-page":"0","volume":"14","author":"Dubov M.","year":"1978","journal-title":"Differentsial rime nye Uravneniya"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00941158"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500030742"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(67)90039-3"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021737526541"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:1997104"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(94)E0082-R"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1070\/SM1995v186n06ABEH000047"},{"key":"R20","first-page":"751","volume":"9","author":"Khapalov Alexander","year":"1999","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"R21","first-page":"153","volume":"29","author":"Klamka J.","year":"2000","journal-title":"Control Cybernet."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511574801"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1109\/9.920790"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7386"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1080\/00207178908559721"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/0325040"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/0325064"},{"key":"R29","volume-title":"Monotone operators in Banach space and nonlinear partial differential equations","author":"Showalter R.","year":"1997"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(01)00158-X"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1137\/0313028"},{"key":"R32","unstructured":"N.Vakhaniya, V.Tarieladze, S.Chobanyan, Veroyatnostnye raspredeleniya v banakhovykh prostranstvakh, \u201cNauka\u201d, 1985, 368\u2013086j:60014"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940936"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4260-4"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1137\/0321033"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2002.8.469"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012901391688","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:24:18Z","timestamp":1787318658000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012901391688"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0363012901391688"],"URL":"https:\/\/doi.org\/10.1137\/s0363012901391688","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}