{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:53Z","timestamp":1740134573150,"version":"3.37.3"},"reference-count":40,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"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":["11371384","cstc2013jcyjA0940","2013ABA2036"],"award-info":[{"award-number":["11371384","cstc2013jcyjA0940","2013ABA2036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005230","name":"Natural Science Foundation of Chongqing","doi-asserted-by":"publisher","award":["11371384","cstc2013jcyjA0940","2013ABA2036"],"award-info":[{"award-number":["11371384","cstc2013jcyjA0940","2013ABA2036"]}],"id":[{"id":"10.13039\/501100005230","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Fuling","award":["11371384","cstc2013jcyjA0940","2013ABA2036"],"award-info":[{"award-number":["11371384","cstc2013jcyjA0940","2013ABA2036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We study the Cauchy problem of a weakly dissipative modified two-component Camassa-Holm equation. We firstly establish the local well-posedness result. Then we present a precise blow-up scenario. Moreover, we obtain several blow-up results and the blow-up rate of strong solutions. Finally, we consider the asymptotic behavior of solutions.<\/jats:p>","DOI":"10.1155\/2013\/547261","type":"journal-article","created":{"date-parts":[[2013,9,11]],"date-time":"2013-09-11T17:01:35Z","timestamp":1378918895000},"page":"1-11","source":"Crossref","is-referenced-by-count":1,"title":["Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation"],"prefix":"10.1155","volume":"2013","author":[{"given":"Yongsheng","family":"Mi","sequence":"first","affiliation":[{"name":"College of Mathematics and Computer Sciences, Yangtze Normal University, Chongqing, Fuling 408100, China"},{"name":"College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China"}]},{"given":"Chunlai","family":"Mu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.71.1661"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-005-0041-7"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.01.027"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1080\/03605300601088674"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2009.24.1047"},{"key":"44","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2003.12.030"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-011-9115-0"},{"key":"45","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.12.005"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2008.10.050"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/2\/004"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2007.19.493"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.08.002"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2010.11.015"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2009.12.597"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-009-0660-2"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2009.06.011"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210509001218"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/s00605-011-0293-5"},{"volume":"79","journal-title":"Physical Review E","year":"2009","key":"19"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2011.30.1161"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-010-0483-9"},{"key":"42","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2011.569495"},{"key":"9","first-page":"199","volume-title":"Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation, Nonlinear partial differential equations and hyperbolic wave phenomena","volume":"526","year":"2010"},{"key":"39","doi-asserted-by":"publisher","DOI":"10.1063\/1.3562928"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s11040-011-9089-z"},{"key":"40","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2011.04.015"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2011.06.013"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2011.09.041"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2011.08.024"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/736765"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-008-6207-3"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(88)90010-1"},{"issue":"8","key":"27","volume":"50","year":"2009","journal-title":"Journal of Mathematical Physics"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2011.621893"},{"issue":"10","key":"24","volume":"52","year":"2011","journal-title":"Journal of Mathematical Physics"},{"first-page":"25","volume-title":"Quasi-linear equations of evolution with application to partial differential equations","year":"1975","key":"30"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392586"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2011-10922-5"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-006-0172-4"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.01.030"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/547261.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/547261.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/547261.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T08:56:10Z","timestamp":1469868970000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/547261\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":40,"alternative-id":["547261","547261"],"URL":"https:\/\/doi.org\/10.1155\/2013\/547261","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}