{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:39:05Z","timestamp":1787323145197,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We analyze the controllability properties of systems which provide a description, at first approximation, of a kind of viscoelastic fluid. We consider linear Maxwell fluids. First, we establish the large time approximate-finite dimensional controllability of the system, with distributed or boundary controls supported by arbitrary small sets. Then, we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets. The proofs of these results rely on classical arguments. In particular, the approximate controllability result is implied by appropriate unique continuation properties, while exact controllability is a consequence of observability (inverse) inequalities. We also discuss questions concerning the controllability of viscoelastic fluids and some related open problems.<\/jats:p>","DOI":"10.1137\/100813592","type":"journal-article","created":{"date-parts":[[2012,4,17]],"date-time":"2012-04-17T18:24:15Z","timestamp":1334687055000},"page":"900-924","source":"Crossref","is-referenced-by-count":15,"title":["Some Controllability Results for Linear Viscoelastic Fluids"],"prefix":"10.1137","volume":"50","author":[{"given":"J.L.","family":"Boldrini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Doubova","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Fern\u00e1ndez-Cara","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Gonz\u00e1lez-Burgos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0330055"},{"key":"R2","unstructured":"L. Bers, F. John, and M. Schechter,\n                      Partial Differential Equations\n                      , John Wiley & Sons, New York, 1964."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:1996102"},{"key":"R4","first-page":"429","volume":"4","author":"Coron J.-M.","year":"1996","journal-title":"Russ. J. Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/1061-9208","issn-type":"print"},{"key":"R5","unstructured":"R. Dautray and J.L. Lions,\n                      Mathematical Analysis and Numerical Methods for Science and Technology, Vol.\n                      6:\n                      Evolution Problems,\n                      Springer-Verlag, Berlin, 1993."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:1996109"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1080\/03605309608821198"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2004.02.010"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/04061965X"},{"key":"R10","first-page":"565","volume":"3","author":"Fursikov A.V.","year":"1999","journal-title":"Uspekhi Mat. Nauk, 3 (1999), pp. 93\u2013146 (in Russian); Russian Math. Surveys"},{"key":"R11","first-page":"443","volume":"302","author":"Ho L.F.","year":"1986","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-4442","issn-type":"print"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:1998104"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"D.D. Joseph,\n                      Fluid Dynamics of Viscoelastic Liquids,\n                      Appl. Math. Sci. 84, Springer-Verlag, New York, 1990.","DOI":"10.1007\/978-1-4612-4462-2"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/1030001"},{"key":"R15","unstructured":"J.L. Lions,\n                      Contr\u00f4labilit\u00e9 exacte perturbation et stabilisation de syst\u00e8mes distribu\u00e9s,\n                      Tomes 1, 2, Contr\u00f4labilit\u00e9 exacte, Masson, Paris, 1988."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012998345615"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"A. Pazy,\n                      Semigroups of Linear Operators and Applications to Partial Differential Equations,\n                      Appl. Math. Sci. 44, Springer-Verlag, New York, 1983.","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"R18","unstructured":"J.P. Puel,\n                      Application of Carleman inequalities to controllability and inverse problems,\n                      Textos Metodos Mat. Instituto de Matematica de l'UFRJ, to appear."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2005.04.006"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnnfm.2005.08.008"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.200610313"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2008.10.006"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnnfm.2008.06.010"},{"key":"R24","unstructured":"M. Renardy, W.J. Hrusa, and J.A. Nohel,\n                      Mathematical problems in viscoelasticity,\n                      Pitman Monogr. Surveys in Pure and Appl. Math. 35, Longman Scientific & Technical, Essex, UK, 1987."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnnfm.2009.10.006"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"K. Yosida,\n                      Functional Analysis,\n                      Classics Math., Springer-Verlag, Berlin, 1995.","DOI":"10.1007\/978-3-642-61859-8"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2000.0553"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(97)89951-5"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100813592","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:44:27Z","timestamp":1787319867000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100813592"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1137\/100813592"],"URL":"https:\/\/doi.org\/10.1137\/100813592","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}