{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:38:37Z","timestamp":1753886317288,"version":"3.41.2"},"reference-count":31,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,7,15]],"date-time":"2012-07-15T00:00:00Z","timestamp":1342310400000},"content-version":"vor","delay-in-days":196,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100002467","name":"Dankook University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002467","id-type":"DOI","asserted-by":"publisher"}]}],"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>A blow\u2010up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow\u2010up time is presented. It is pointed out that the upper bound of the first blow\u2010up time depends on the support of the initial datum.<\/jats:p>","DOI":"10.1155\/2012\/202137","type":"journal-article","created":{"date-parts":[[2012,7,15]],"date-time":"2012-07-15T21:02:40Z","timestamp":1342386160000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Blow\u2010Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity"],"prefix":"10.1155","volume":"2012","author":[{"given":"Hee Chul","family":"Pak","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,15]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.5802\/afst.600"},{"key":"e_1_2_5_2_2","first-page":"73","article-title":"Nonlinear parabolic equations involving measures as initial conditions","volume":"62","author":"Br\u00e9zis H.","year":"1983","journal-title":"Journal de Math\u00e9matiques Pures et Appliqu\u00e9es. Neuvi\u00e8me S\u00e9rie"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251357"},{"volume-title":"An Introduction to Semilinear Evolution Equations","year":"1988","author":"Cazenave T.","key":"e_1_2_5_4_2"},{"volume-title":"Partial Differential Equations of Parabolic Type","year":"1964","author":"Friedman A.","key":"e_1_2_5_5_2"},{"key":"e_1_2_5_6_2","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1982.31.31016"},{"key":"e_1_2_5_7_2","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/023"},{"key":"e_1_2_5_8_2","first-page":"757","article-title":"Continuity of the blow-up time and a priori bounds for solutions in superlinear parabolic problems","volume":"29","author":"Quittner P.","year":"2003","journal-title":"Houston Journal of Mathematics"},{"key":"e_1_2_5_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2003.10.007"},{"key":"e_1_2_5_10_2","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1980.29.29007"},{"key":"e_1_2_5_11_2","first-page":"363","article-title":"On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources","volume":"18","author":"Andreucci D.","year":"1991","journal-title":"Annali della Scuola Normale Superiore di Pisa. Classe di Scienze"},{"key":"e_1_2_5_12_2","first-page":"189","volume-title":"\u00c9quations aux D\u00e9riv\u00e9es Partielles et Applications","author":"Bidaut-V\u00e9ron M.-F.","year":"1998"},{"key":"e_1_2_5_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.06.022"},{"key":"e_1_2_5_14_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2000.0648"},{"key":"e_1_2_5_15_2","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1985.34.34025"},{"key":"e_1_2_5_16_2","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1987.36.36001"},{"key":"e_1_2_5_17_2","first-page":"141","article-title":"Explosion de solutions d\u2032\u00e9quations paraboliques semilin\u00e9aires supercritiques","volume":"319","author":"Herrero M. A.","year":"1994","journal-title":"Comptes Rendus de l\u2032Acad\u00e9mie des Sciences"},{"key":"e_1_2_5_18_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2006.14.169"},{"key":"e_1_2_5_19_2","doi-asserted-by":"crossref","first-page":"615","DOI":"10.57262\/ade\/1355926843","article-title":"Universal blow-up rates for a semilinear heat equation and applications","volume":"8","author":"Matos J.","year":"2003","journal-title":"Advances in Differential Equations"},{"key":"e_1_2_5_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s000390050123"},{"key":"e_1_2_5_21_2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160380303"},{"key":"e_1_2_5_22_2","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/13\/4\/311"},{"key":"e_1_2_5_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(87)90020-6"},{"key":"e_1_2_5_24_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199701)50:1&lt;1::AID-CPA1&gt;3.3.CO;2-R"},{"key":"e_1_2_5_25_2","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/41.3.207"},{"key":"e_1_2_5_26_2","doi-asserted-by":"crossref","first-page":"79","DOI":"10.3233\/ASY-2004-597","article-title":"Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem","volume":"37","author":"Groisman P.","year":"2004","journal-title":"Asymptotic Analysis"},{"key":"e_1_2_5_27_2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160450303"},{"key":"e_1_2_5_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.09.044"},{"key":"e_1_2_5_29_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970463"},{"key":"e_1_2_5_30_2","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/019"},{"key":"e_1_2_5_31_2","series-title":"Pure and Applied Mathematics","volume-title":"Eigenvalues in Riemannian Geometry","author":"Chavel I.","year":"1984"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/202137.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/202137.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/202137","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T05:20:52Z","timestamp":1743744052000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/202137"}},"subtitle":[],"editor":[{"given":"Juli\u00e1n","family":"L\u00f3pez-G\u00f3mez","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/202137"],"URL":"https:\/\/doi.org\/10.1155\/2012\/202137","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":"2012-04-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-06-11","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-07-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"202137"}}