{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:56:32Z","timestamp":1753883792649,"version":"3.41.2"},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,8,10]],"date-time":"2012-08-10T00:00:00Z","timestamp":1344556800000},"content-version":"vor","delay-in-days":222,"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":["11071185","09JCYBJC01800"],"award-info":[{"award-number":["11071185","09JCYBJC01800"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006606","name":"Natural Science Foundation of Tianjin","doi-asserted-by":"crossref","award":["11071185","09JCYBJC01800"],"award-info":[{"award-number":["11071185","09JCYBJC01800"]}],"id":[{"id":"10.13039\/501100006606","id-type":"DOI","asserted-by":"crossref"}]}],"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 investigate the global existence of the delayed nonlinear evolutionary equation <jats:italic>\u2202<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub><jats:italic>u<\/jats:italic> + <jats:italic>A<\/jats:italic><jats:italic>u<\/jats:italic> = <jats:italic>f<\/jats:italic>(<jats:italic>u<\/jats:italic>(<jats:italic>t<\/jats:italic>), <jats:italic>u<\/jats:italic>(<jats:italic>t<\/jats:italic> \u2212 <jats:italic>\u03c4<\/jats:italic>)). Our work space is the fractional powers space <jats:italic>X<\/jats:italic><jats:sup><jats:italic>\u03b1<\/jats:italic><\/jats:sup>. Under the fundamental  theorem on sectorial operators, we make use of the fixed\u2010point principle to prove the local existence and uniqueness theorem. Then, the global existence is obtained by Gronwall\u2019s inequality.<\/jats:p>","DOI":"10.1155\/2012\/257140","type":"journal-article","created":{"date-parts":[[2012,8,10]],"date-time":"2012-08-10T21:00:39Z","timestamp":1344632439000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Global Existence of  Nonlinear Evolutionary Equation with Small Delay"],"prefix":"10.1155","volume":"2012","author":[{"given":"Xunwu","family":"Yin","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,8,10]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"e_1_2_5_2_2","series-title":"Graduate Studies in Mathematics","volume-title":"Partial Differential Equation","author":"Evans L. C.","year":"1998"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089647"},{"key":"e_1_2_5_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5037-9"},{"key":"e_1_2_5_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01063736"},{"key":"e_1_2_5_6_2","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/142128"},{"key":"e_1_2_5_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-00547-7"},{"key":"e_1_2_5_8_2","series-title":"Mathematical Surveys and Monographs","volume-title":"Asymptotic Behavior of Dissipative Systems","author":"Hale J. K.","year":"1988"},{"key":"e_1_2_5_9_2","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195188180"},{"key":"e_1_2_5_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(78)90037-2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/257140.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/257140.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/257140","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:46:03Z","timestamp":1718088363000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/257140"}},"subtitle":[],"editor":[{"given":"Yonghong","family":"Yao","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/257140"],"URL":"https:\/\/doi.org\/10.1155\/2012\/257140","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":"2012-04-11","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":"2012-08-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"257140"}}