{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:43:09Z","timestamp":1753886589041,"version":"3.41.2"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,2,16]],"date-time":"2012-02-16T00:00:00Z","timestamp":1329350400000},"content-version":"vor","delay-in-days":46,"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":["J1030101"],"award-info":[{"award-number":["J1030101"]}],"id":[{"id":"10.13039\/501100001809","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>The existence of weak solutions is studied to the initial Dirichlet problem\nof the equation <jats:italic>u<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> = <jats:italic>u<\/jats:italic>div(|\u2207<jats:italic>u<\/jats:italic>|<jats:sup><jats:italic>p<\/jats:italic>(<jats:italic>x<\/jats:italic>)\u22122<\/jats:sup>\u2207<jats:italic>u<\/jats:italic>), with inf <jats:italic>p<\/jats:italic>(<jats:italic>x<\/jats:italic>) &gt; 2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.<\/jats:p>","DOI":"10.1155\/2012\/835495","type":"journal-article","created":{"date-parts":[[2012,2,16]],"date-time":"2012-02-16T21:02:27Z","timestamp":1329426147000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence of Solutions for the Evolution <i>p<\/i>(<i>x<\/i>)\u2010Laplacian Equation Not in Divergence Form"],"prefix":"10.1155","volume":"2012","author":[{"given":"Changchun","family":"Liu","sequence":"first","affiliation":[]},{"given":"Junchao","family":"Gao","sequence":"additional","affiliation":[]},{"given":"Songzhe","family":"Lian","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,2,16]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(87)90099-4"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/937079"},{"key":"e_1_2_6_3_2","first-page":"189","article-title":"Existence and nonuniqueness of weak solutions of the initial-boundary value problem for u\n                  \n                     t\n                   = u\n                  \n                     \u03c3\n                  div(|\u2207u|\n                     p\u22122\u2207u)","volume":"21","author":"Zhou W.","year":"2005","journal-title":"Northeastern Mathematical Journal"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2004.09.053"},{"key":"e_1_2_6_5_2","first-page":"291","article-title":"Some results on a class of nonlinear degenerate parabolic equations not in divergence form","volume":"19","author":"Zhou W.","year":"2003","journal-title":"Northeastern Mathematical Journal"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0294-1449(03)00031-3"},{"key":"e_1_2_6_7_2","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.57262\/ade\/1355867817","article-title":"Higher integrability for parabolic equations of p(x, t)-Laplacian type","volume":"10","author":"Antontsev S.","year":"2005","journal-title":"Advances in Differential Equations"},{"key":"e_1_2_6_8_2","first-page":"33","volume-title":"Free boundary problems","author":"Antontsev S.","year":"2007"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.07.019"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.5565\/PUBLMAT_53209_04"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0104029"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/814103"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-002-0208-7"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2007.01.008"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(02)00150-5"},{"key":"e_1_2_6_16_2","doi-asserted-by":"publisher","DOI":"10.1070\/SM1993v076n02ABEH003421"},{"key":"e_1_2_6_17_2","doi-asserted-by":"publisher","DOI":"10.1070\/SM1993v076n02ABEH003421"},{"key":"e_1_2_6_18_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7617"},{"key":"e_1_2_6_19_2","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/023"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/835495.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/835495.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/835495","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:45:18Z","timestamp":1718088318000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/835495"}},"subtitle":[],"editor":[{"given":"Hui-Shen","family":"Shen","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/835495"],"URL":"https:\/\/doi.org\/10.1155\/2012\/835495","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":"2011-10-31","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-12-06","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-02-16","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"835495"}}