{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T23:19:49Z","timestamp":1783034389414,"version":"3.54.6"},"reference-count":33,"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":["11272277"],"award-info":[{"award-number":["11272277"]}],"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":["11226188"],"award-info":[{"award-number":["11226188"]}],"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":["2013ZZGH027"],"award-info":[{"award-number":["2013ZZGH027"]}],"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":["11272277"],"award-info":[{"award-number":["11272277"]}],"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":["11226188"],"award-info":[{"award-number":["11226188"]}],"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":["2013ZZGH027"],"award-info":[{"award-number":["2013ZZGH027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Central Universities","award":["11272277"],"award-info":[{"award-number":["11272277"]}]},{"name":"Central Universities","award":["11226188"],"award-info":[{"award-number":["11226188"]}]},{"name":"Central Universities","award":["2013ZZGH027"],"award-info":[{"award-number":["2013ZZGH027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>The goal of this paper is to study an initial boundary value problem of stochastic viscoelastic wave equation with nonlinear damping and source terms. Under certain conditions on the initial data: the relaxation function, the indices of nonlinear damping, and source terms and the random force, we prove the local existence and uniqueness of solution by the Galerkin approximation method. Then, considering the relationship between the indices of nonlinear damping and nonlinear source, we give the necessary conditions of global existence and explosion in finite time in some sense of solutions, respectively.<\/jats:p>","DOI":"10.1155\/2014\/450289","type":"journal-article","created":{"date-parts":[[2014,3,30]],"date-time":"2014-03-30T03:59:04Z","timestamp":1396151944000},"page":"1-15","source":"Crossref","is-referenced-by-count":3,"title":["Stochastic Viscoelastic Wave Equations with Nonlinear Damping and Source Terms"],"prefix":"10.1155","volume":"2014","author":[{"given":"Shuilin","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yantao","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanbin","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"issue":"2","key":"12","first-page":"191","volume":"150","year":"1988","journal-title":"Archive for Rational Mechanics and Analysis"},{"issue":"4","key":"14","first-page":"713","volume":"30","year":"1989","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/28.4.473"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01109723"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1137\/0505015"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1998.6126"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1994.1051"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2009.2.583"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.5269\/bspm.v25i1-2.7427"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2007.07.004"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200310104"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.07.022"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.02.015"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(95)00119-G"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/s005260100096"},{"issue":"1","key":"6","first-page":"85","volume":"14","year":"2001","journal-title":"Differential and Integral Equations"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.04.011"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2013-11869-1"},{"key":"5","year":"2007"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/403528"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511666223"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/415764"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/279509"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1002\/mana.201300114"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2013.12.1111"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2012.04.004"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2007.10.016"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1142\/S0219025713500136"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/s11401-009-0170-x"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1142\/S0129055X11004461"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-007-9029-2"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"20","year":"1969"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/450289.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/450289.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/450289.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T19:30:21Z","timestamp":1469734221000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/450289\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":33,"alternative-id":["450289","450289"],"URL":"https:\/\/doi.org\/10.1155\/2014\/450289","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}