{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T18:06:54Z","timestamp":1732039614268},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,9,9]],"date-time":"2020-09-09T00:00:00Z","timestamp":1599609600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,9,9]],"date-time":"2020-09-09T00:00:00Z","timestamp":1599609600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s11424-020-9082-3","type":"journal-article","created":{"date-parts":[[2020,9,10]],"date-time":"2020-09-10T11:42:31Z","timestamp":1599738151000},"page":"537-551","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Approximate Controllability for Degenerate Heat Equation with Bilinear Control"],"prefix":"10.1007","volume":"34","author":[{"given":"Lingfei","family":"Li","sequence":"first","affiliation":[]},{"given":"Hang","family":"Gao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,9]]},"reference":[{"issue":"8","key":"9082_CR1","doi-asserted-by":"publisher","first-page":"2395","DOI":"10.1016\/j.jde.2009.07.026","volume":"247","author":"X Fu","year":"2009","unstructured":"Fu X, Yong J, and Zhang X, Controllability and observability of a heat equation with hyperbolic memory kernel, J. Differential Equations, 2009, 247(8): 2395\u20132439.","journal-title":"J. Differential Equations"},{"issue":"1\u20132","key":"9082_CR2","first-page":"81","volume":"21","author":"X Zhang","year":"2008","unstructured":"Zhang X, Unique continuation for stochastic parabolic equations, Differential Integral Equations, 2008, 21(1\u20132): 81\u201393.","journal-title":"Differential Integral Equations"},{"issue":"2","key":"9082_CR3","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1137\/070685786","volume":"40","author":"X Zhang","year":"2008","unstructured":"Zhang X, Carleman and observability estimates for stochastic wave equations, SIAM J. Math. Anal., 2008, 40(2): 851\u2013868.","journal-title":"SIAM J. Math. Anal."},{"key":"9082_CR4","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/j.automatica.2017.10.004","volume":"87","author":"Q Zhu","year":"2018","unstructured":"Zhu Q and Wang H, Output feedback stabilization of stochastic feedforward systems with unknown control coefficients and unknown output function, Automatica, 2018, 87: 166\u2013175.","journal-title":"Automatica"},{"key":"9082_CR5","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.automatica.2018.04.016","volume":"94","author":"B Wang","year":"2018","unstructured":"Wang B and Zhu Q, Stability analysis of semi-Markov switched stochastic systems, Automatica, 2018, 94: 72\u201380.","journal-title":"Automatica"},{"key":"9082_CR6","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.automatica.2018.09.026","volume":"98","author":"H Wang","year":"2018","unstructured":"Wang H and Zhu Q, Adaptive output feedback control of stochastic nonholonomic systems with nonlinear parameterization, Automatica, 2018, 98: 247\u2013255.","journal-title":"Automatica"},{"key":"9082_CR7","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.sysconle.2019.05.004","volume":"129","author":"M Zhang","year":"2019","unstructured":"Zhang M and Zhu Q, New criteria of input-to-state stability for nonlinear switched stochastic delayed systems with asynchronous switching, Syst. Control Lett., 2019, 129: 43\u201350.","journal-title":"Syst. Control Lett."},{"key":"9082_CR8","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.sysconle.2018.05.015","volume":"118","author":"Q Zhu","year":"2018","unstructured":"Zhu Q, Stability analysis of stochastic delay differential equations with L\u00e9vy noise, Syst. Control Lett., 2018, 118: 62\u201368.","journal-title":"Syst. Control Lett."},{"issue":"4","key":"9082_CR9","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1137\/0320042","volume":"20","author":"J M Ball","year":"1982","unstructured":"Ball J M, Marsden J E, and Slemrod M, Controllability for distributed bilinear systems, SIAM J. Control Optim., 1982, 20(4): 575\u2013597.","journal-title":"SIAM J. Control Optim."},{"issue":"4","key":"9082_CR10","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/0167-6911(94)00022-N","volume":"24","author":"K Kime","year":"1995","unstructured":"Kime K, Simultaneous control of a rod equation and a simple Schr\u00f6dinger equation, Syst. Control Lett., 1995, 24(4): 301\u2013306.","journal-title":"Syst. Control Lett."},{"key":"9082_CR11","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1051\/cocv:2002011","volume":"7","author":"A Y Khapalov","year":"2002","unstructured":"Khapalov A Y, Global non-negative controllability of the semilinear parabolic equation governed by bilinear control, ESAIM Control Optim. Calc. Var., 2002, 7: 269\u2013283.","journal-title":"ESAIM Control Optim. Calc. Var."},{"issue":"6","key":"9082_CR12","doi-asserted-by":"publisher","first-page":"1886","DOI":"10.1137\/S0363012901394607","volume":"41","author":"A Y Khapalov","year":"2003","unstructured":"Khapalov A Y, Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: A qualitative approach, SIAM J. Control Optim., 2003, 41(6): 1886\u20131900.","journal-title":"SIAM J. Control Optim."},{"issue":"4","key":"9082_CR13","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1016\/j.matpur.2017.07.002","volume":"108","author":"P Cannarsa","year":"2017","unstructured":"Cannarsa P, Floridia G, and Khapalov A Y, Multiplicative controllability for semilinear reaction-diffusion equations with finitely many changes of sign, Journal de Math\u00e9matiques Pures et Appliqu\u00e9es, 2017, 108(4): 425\u2013458.","journal-title":"Journal de Math\u00e9matiques Pures et Appliqu\u00e9es"},{"issue":"4","key":"9082_CR14","first-page":"1293","volume":"14","author":"P Cannarsa","year":"2010","unstructured":"Cannarsa P and Khapalov A Y, Multiplicative controllability for reaction-diffusion equations with target states admitting finitely many changes of sign, Discrete Contin. Dyn. Syst. Ser. B, 2010, 14(4): 1293\u20131311.","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"issue":"1","key":"9082_CR15","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.aml.2009.07.025","volume":"23","author":"P Lei","year":"2010","unstructured":"Lei P and Gao H, Null controllability of semilinear parabolic equations via the bilinear control, Appl. Math. Lett., 2010, 23(1): 53\u201357.","journal-title":"Appl. Math. Lett."},{"issue":"1","key":"9082_CR16","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1002\/zamm.200510292","volume":"87","author":"P Lin","year":"2007","unstructured":"Lin P, Lei P, and Gao H, Bilinear control system with the reaction-diffusion term satisfying Newton\u2019s law, Z. angew. Math. Mech., 2007, 87(1): 14\u201323.","journal-title":"Z. angew. Math. Mech."},{"issue":"6","key":"9082_CR17","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1016\/j.aml.2005.05.016","volume":"19","author":"P Lin","year":"2006","unstructured":"Lin P, Zhou Z, and Gao H, Exact controllability of the parabolic system with bilinear control, Appl. Math. Lett., 2006, 19(6): 568\u2013575.","journal-title":"Appl. Math. Lett."},{"issue":"18","key":"9082_CR18","doi-asserted-by":"publisher","first-page":"5074","DOI":"10.1002\/mma.3428","volume":"38","author":"M Ouzahra","year":"2015","unstructured":"Ouzahra M, Tsouli A, and Boutoulout A, Exact controllability of the heat equation with bilinear control, Mathematical Methods in the Applied Sciences, 2015, 38(18): 5074\u20135084.","journal-title":"Mathematical Methods in the Applied Sciences"},{"key":"9082_CR19","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.ejcon.2016.05.004","volume":"32","author":"M Ouzahra","year":"2016","unstructured":"Ouzahra M, Approximate and exact controllability of a reaction-diffusion equation governed by bilinear control, European Journal of Control, 2016, 32: 32\u201338.","journal-title":"European Journal of Control"},{"issue":"2","key":"9082_CR20","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s00028-006-0222-6","volume":"6","author":"F Alabau-Boussouira","year":"2006","unstructured":"Alabau-Boussouira F, Cannarsa P, and Fragnelli G, Carleman estimates for degenerate parabolic operators with applications to null controllability, J. Evol. Equ., 2006, 6(2): 161\u2013204.","journal-title":"J. Evol. Equ."},{"issue":"1","key":"9082_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/04062062X","volume":"47","author":"P Cannarsa","year":"2008","unstructured":"Cannarsa P, Martinez P, and Vancostenoble J, Carleman estimates for a class of degenerate parabolic operators, SIAM J. Control Optim., 2008, 47(1): 1\u201319.","journal-title":"SIAM J. Control Optim."},{"issue":"4","key":"9082_CR22","doi-asserted-by":"publisher","first-page":"607","DOI":"10.3934\/cpaa.2004.3.607","volume":"3","author":"P Cannarsa","year":"2004","unstructured":"Cannarsa P, Martinez P, and Vancostenoble J, Persistent regional null controllability for a class of degenerate parabolic equations, Communications on Pure and Applied Analysis, 2004, 3(4): 607\u2013635.","journal-title":"Communications on Pure and Applied Analysis"},{"issue":"4","key":"9082_CR23","doi-asserted-by":"publisher","first-page":"2037","DOI":"10.1137\/120901374","volume":"52","author":"M Gueye","year":"2014","unstructured":"Gueye M, Exact boundary controllability of 1-D parabolic and hyperbolic degenerate equations, SIAM J. Control Optim., 2014, 52(4): 2037\u20132054.","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"9082_CR24","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s00028-009-0044-4","volume":"10","author":"C Wang","year":"2010","unstructured":"Wang C, Approximate controllability of a class of semilinear systems with boundary degeneracy, J. Evol. Equ., 2010, 10(1): 163\u2013193.","journal-title":"J. Evol. Equ."},{"issue":"1","key":"9082_CR25","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1016\/j.amc.2008.04.056","volume":"203","author":"C Wang","year":"2008","unstructured":"Wang C, Approximate controllability of a class of degenerate systems, Applied Mathematics and Computation, 2008, 203(1): 447\u2013456.","journal-title":"Applied Mathematics and Computation"},{"issue":"2","key":"9082_CR26","doi-asserted-by":"publisher","first-page":"1149","DOI":"10.1016\/j.jmaa.2006.03.079","volume":"326","author":"P Lin","year":"2007","unstructured":"Lin P, Gao H, and Liu X, Some results on a nonlinear degenerate parabolic system by bilinear control, J. Math. Anal. Appl., 2007, 326(2): 1149\u20131160.","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"9082_CR27","first-page":"1","volume":"2","author":"P Cannarsa","year":"2011","unstructured":"Cannarsa P and Floridia G, Approximate multiplicative controllability for degenerate parabolic problems with Robin boundary conditions, Commun. Appl. Ind. Math., 2011, 2(2): 1\u201316.","journal-title":"Commun. Appl. Ind. Math."},{"issue":"9","key":"9082_CR28","doi-asserted-by":"publisher","first-page":"3382","DOI":"10.1016\/j.jde.2014.06.016","volume":"257","author":"G Floridia","year":"2014","unstructured":"Floridia G, Approximate controllability for nonlinear degenerate parabolic problems with bilinear control, J. Differential Equations, 2014, 257(9): 3382\u20133422.","journal-title":"J. Differential Equations"},{"issue":"4","key":"9082_CR29","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1051\/cocv\/2012004","volume":"18","author":"L A Fern\u00e1ndez","year":"2012","unstructured":"Fern\u00e1ndez L A and Khapalov A Y, Controllability properties for the one-dimensional heat equation under multiplicative or nonnegative additive controls with local mobile support, ESAIM Control Optim. Calc. Var., 2012, 18(4): 1207\u20131224.","journal-title":"ESAIM Control Optim. Calc. Var."},{"issue":"1","key":"9082_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/PL00005959","volume":"57","author":"M Campiti","year":"1998","unstructured":"Campiti M, Metafune G, and Pallara D, Degenerate self-adjoint evolution equations on the unit interval, Semigroup Forum, 1998, 57(1): 1\u201336.","journal-title":"Semigroup Forum"},{"key":"9082_CR31","volume-title":"Transl. Math. Mono.","author":"O A Lady\u017ehenskaya","year":"1968","unstructured":"Lady\u017ehenskaya O A, Solonnikov V A, and Ural\u2019ceva N N, Linear and quasilinear equations of parabolic type, Transl. Math. Mono., vol. 23, AMS, Providence R.I., 1968."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-020-9082-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-020-9082-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-020-9082-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T23:44:19Z","timestamp":1631144659000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-020-9082-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,9]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["9082"],"URL":"https:\/\/doi.org\/10.1007\/s11424-020-9082-3","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,9]]},"assertion":[{"value":"10 March 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}