{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:14Z","timestamp":1740134534757,"version":"3.37.3"},"reference-count":27,"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":["11271218"],"award-info":[{"award-number":["11271218"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>d<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mi>d<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mi>\ud835\udc9c<\/mml:mi><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>+<\/mml:mo><mml:mi>\u212c<\/mml:mi><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>\u220b<\/mml:mo><mml:mi>f<\/mml:mi><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:math>in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msup><mml:mrow><mml:mi>V<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>t<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mfenced close=\"]\" separators=\"|\"><mml:mrow><mml:mn>0<\/mml:mn><mml:mo>,<\/mml:mo><mml:mi>\u00a0<\/mml:mi><mml:mi>T<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>V<\/mml:mi><\/mml:mrow><\/mml:math>is a real reflexive Banach space,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>\ud835\udc9c<\/mml:mi><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>\u212c<\/mml:mi><\/mml:mrow><\/mml:math>are maximal monotone operators (possibly multivalued) from<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>V<\/mml:mi><\/mml:mrow><\/mml:math>to its dual<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:msup><mml:mrow><mml:mi>V<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>. In view of some practical applications, we assume that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>\ud835\udc9c<\/mml:mi><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi>\u212c<\/mml:mi><\/mml:mrow><\/mml:math>are subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:mi>\ud835\udc9c<\/mml:mi><\/mml:mrow><\/mml:math>and the coerciveness of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:mi>\u212c<\/mml:mi><\/mml:mrow><\/mml:math>. As an application, we give the existence for a nonlinear degenerate parabolic equation.<\/jats:p>","DOI":"10.1155\/2014\/567241","type":"journal-article","created":{"date-parts":[[2014,4,24]],"date-time":"2014-04-24T17:12:29Z","timestamp":1398359549000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation"],"prefix":"10.1155","volume":"2014","author":[{"given":"Ning","family":"Su","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3682-3853","authenticated-orcid":true,"given":"Li","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"journal-title":"Discrete and Continuous Dynamical Systems A","first-page":"30","year":"2005","key":"2"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-004-0162-y"},{"volume":"49","year":"1997","key":"21"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1002\/mma.276"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1002\/mma.541"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2003.10.029"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2006.04.006"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01176474"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/0510052"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1137\/0512062"},{"key":"17","first-page":"1","volume":"30","year":"1981","journal-title":"Bulletin of the Faculty of Education. Chiba University"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(86)90058-1"},{"issue":"2","key":"19","first-page":"301","volume":"32","year":"1989","journal-title":"Funkcialaj Ekvacioj"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2001.1.403"},{"issue":"3","key":"26","first-page":"491","volume":"23","year":"1976","journal-title":"Journal of the Faculty of Science. University of Tokyo"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/03140623"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.0155"},{"year":"2006","key":"5"},{"year":"1976","key":"7"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-5542-5"},{"key":"12"},{"volume":"8","year":"2008","key":"13"},{"year":"1976","key":"15"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761596"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1137\/070684574"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2003.06.002"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1002\/mma.763"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/567241.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/567241.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/567241.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T22:13:06Z","timestamp":1469743986000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/567241\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":27,"alternative-id":["567241","567241"],"URL":"https:\/\/doi.org\/10.1155\/2014\/567241","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}