{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:49:02Z","timestamp":1753886942001,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,7,12]],"date-time":"2012-07-12T00:00:00Z","timestamp":1342051200000},"content-version":"vor","delay-in-days":193,"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":["11071177","2010JY0057"],"award-info":[{"award-number":["11071177","2010JY0057"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Sichuan","award":["11071177","2010JY0057"],"award-info":[{"award-number":["11071177","2010JY0057"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We consider the global existence of strong solution <jats:italic>u<\/jats:italic>, corresponding to a class of fully nonlinear wave equations with strongly damped terms <jats:italic>u<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><jats:italic>t<\/jats:italic><\/jats:sub> \u2212 <jats:italic>k<\/jats:italic>\u0394<jats:italic>u<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> = <jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic>, \u0394<jats:italic>u<\/jats:italic>) + <jats:italic>g<\/jats:italic>(<jats:italic>x<\/jats:italic>, <jats:italic>u<\/jats:italic>, <jats:italic>D<\/jats:italic><jats:italic>u<\/jats:italic>, <jats:italic>D<\/jats:italic><jats:sup>2<\/jats:sup><jats:italic>u<\/jats:italic>) in a bounded and smooth domain \u03a9 in <jats:italic>R<\/jats:italic><jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>, where <jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic>, \u0394<jats:italic>u<\/jats:italic>) is a given monotone in \u0394<jats:italic>u<\/jats:italic> nonlinearity satisfying some dissipativity and growth restrictions and <jats:italic>g<\/jats:italic>(<jats:italic>x<\/jats:italic>, <jats:italic>u<\/jats:italic>, <jats:italic>D<\/jats:italic><jats:italic>u<\/jats:italic>, <jats:italic>D<\/jats:italic><jats:sup>2<\/jats:sup><jats:italic>u<\/jats:italic>) is in a sense subordinated to <jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic>, \u0394<jats:italic>u<\/jats:italic>). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution .<\/jats:p>","DOI":"10.1155\/2012\/805158","type":"journal-article","created":{"date-parts":[[2012,7,13]],"date-time":"2012-07-13T17:02:46Z","timestamp":1342198966000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms"],"prefix":"10.1155","volume":"2012","author":[{"given":"Zhigang","family":"Pan","sequence":"first","affiliation":[]},{"given":"Hong","family":"Luo","sequence":"additional","affiliation":[]},{"given":"Tian","family":"Ma","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,12]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(80)90040-6"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02102372"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0519024"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.01.025"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.06.018"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.08.011"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2004.3.921"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.07.025"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2006.10.038"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.06.021"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1980-049-5"},{"key":"e_1_2_6_12_2","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.57262\/die\/1367871535","article-title":"Bounded, locally compact global attractors for semilinear damped wave equations on R\n                  \n                     N","volume":"9","author":"Feireisl E.","year":"1996","journal-title":"Differential and Integral Equations"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0645-3"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.06.061"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1186\/1687-2770-2012-42"},{"volume-title":"Theories and Methods in Partial Differential Equations","year":"2011","author":"Ma T.","key":"e_1_2_6_16_2"},{"key":"e_1_2_6_17_2","series-title":"Applied Mathematical Sciences","volume-title":"Applied Functional Analysis: Applications to Mathematical Physics","author":"Zeidler E.","year":"1995"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/805158.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/805158.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/805158","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:43:56Z","timestamp":1718088236000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/805158"}},"subtitle":[],"editor":[{"given":"Kuppalapalle","family":"Vajravelu","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/805158"],"URL":"https:\/\/doi.org\/10.1155\/2012\/805158","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2012-02-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-05-09","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-07-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"805158"}}