{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T20:04:12Z","timestamp":1758398652703,"version":"3.37.3"},"reference-count":4,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171060","11371084","2012187","2013287"],"award-info":[{"award-number":["11171060","11371084","2012187","2013287"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171060","11371084","2012187","2013287"],"award-info":[{"award-number":["11171060","11371084","2012187","2013287"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Department of Education Program of Jilin Province","award":["11171060","11371084","2012187","2013287"],"award-info":[{"award-number":["11171060","11371084","2012187","2013287"]}]},{"name":"Department of Education Program of Jilin Province","award":["11171060","11371084","2012187","2013287"],"award-info":[{"award-number":["11171060","11371084","2012187","2013287"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mn>1<\/mml:mn><mml:mo>-<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:msqrt><mml:mi>e<\/mml:mi><\/mml:msqrt><\/mml:math>, by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability. Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.<\/jats:p>","DOI":"10.1155\/2014\/827698","type":"journal-article","created":{"date-parts":[[2014,3,3]],"date-time":"2014-03-03T08:01:33Z","timestamp":1393833693000},"page":"1-6","source":"Crossref","is-referenced-by-count":4,"title":["Controllability for a Wave Equation with Moving Boundary"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6807-4079","authenticated-orcid":true,"given":"Lizhi","family":"Cui","sequence":"first","affiliation":[{"name":"College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China"},{"name":"School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Libo","family":"Song","sequence":"additional","affiliation":[{"name":"Educational Administration, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"2","key":"1","first-page":"435","volume":"9","year":"1996","journal-title":"Revista Matem\u00e1tica de la Universidad Complutense de Madrid"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1137\/0319010"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.01.062"},{"issue":"4","key":"6","doi-asserted-by":"crossref","first-page":"317","DOI":"10.3233\/ASY-1995-11401","volume":"11","year":"1995","journal-title":"Asymptotic Analysis"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/827698.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/827698.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/827698.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,15]],"date-time":"2020-08-15T22:54:39Z","timestamp":1597532079000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/827698\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":4,"alternative-id":["827698","827698"],"URL":"https:\/\/doi.org\/10.1155\/2014\/827698","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}