{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T13:03:45Z","timestamp":1787663025185,"version":"build-2736575974"},"reference-count":15,"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":[[2002,1]]},"abstract":"<jats:p>We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of ${\\mathbb R}^N$ with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term $f( y, \\nabla y)$ grows slower than $|y| \\log^{3\/2}(1+ |y| + |\\nabla y|) + |\\nabla y| \\log^{1\/2}(1+ |y| + |\\nabla y|)$ at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method.<\/jats:p>","DOI":"10.1137\/s0363012901386465","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"798-819","source":"Crossref","is-referenced-by-count":122,"title":["On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient"],"prefix":"10.1137","volume":"41","author":[{"given":"A.","family":"Doubova","sequence":"first","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"}]},{"given":"E.","family":"Zuazua","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2000105"},{"key":"R2","volume-title":"L\u2019analyse non lin\u00e9aire et ses motivations \u00e9conomiques","author":"Aubin Jean\u2010Pierre","year":"1984"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/s002450010004"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.5802\/afst.543"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500030742"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:1997104"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.57262\/ade\/1356651338"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/s0294-1449(00)00117-7"},{"key":"R9","volume-title":"Controllability of evolution equations","author":"Fursikov A.","year":"1996"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1070\/SM1995v186n06ABEH000047"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"O.Imanuvilov, M.Yamamoto, Carleman estimate for a parabolic equation in a Sobolev space of negative order and its applications, Lecture Notes in Pure and Appl. 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Tech., Harlow, 1991, 357\u201339192k:93029"},{"key":"R15","first-page":"665","volume":"28","author":"Zuazua Enrique","year":"1999","journal-title":"Control Cybernet."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012901386465","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:33:00Z","timestamp":1787319180000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012901386465"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1137\/S0363012901386465"],"URL":"https:\/\/doi.org\/10.1137\/s0363012901386465","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}