{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T14:38:26Z","timestamp":1648823906648},"reference-count":12,"publisher":"Hindawi Limited","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\/501100012226","name":"Youth Science and Technology Innovation Fund of Nanjing Agriculture University","doi-asserted-by":"crossref","award":["KJ2010026","CXLX12_0390","Y0201100265"],"award-info":[{"award-number":["KJ2010026","CXLX12_0390","Y0201100265"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We study the bifurcation and stability of trivial stationary solution<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">0<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn mathvariant=\"normal\">0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">0<\/mml:mn><mml:mo>,<\/mml:mo><mml:mi>L<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>with Neumann's boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the length<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>L<\/mml:mi><\/mml:mrow><\/mml:math>of the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches is studied, and the stability of the bifurcated solutions is analyzed as well.<\/jats:p>","DOI":"10.1155\/2013\/926512","type":"journal-article","created":{"date-parts":[[2013,8,12]],"date-time":"2013-08-12T21:05:17Z","timestamp":1376341517000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model"],"prefix":"10.1155","volume":"2013","author":[{"given":"Lei","family":"Shi","sequence":"first","affiliation":[{"name":"School of Sciences, Nanjing Agricultural University, Nanjing 210095, China"},{"name":"School of Mathematical Sciences and Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"issue":"2","key":"1","doi-asserted-by":"crossref","first-page":"R1473","DOI":"10.1103\/PhysRevE.62.R1473","volume":"62","year":"2000","journal-title":"Physical Review E"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/13\/4\/317"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1137\/06067794X"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1063\/1.868090"},{"issue":"4","key":"5","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1017\/S0022112072001326","volume":"51","year":"1972","journal-title":"Journal of Fluid Mechanics"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/1\/2\/001"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90056-9"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1063\/1.868715"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1063\/1.531986"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409024542"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740100353X"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004176"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/926512.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/926512.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/926512.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,8]],"date-time":"2020-05-08T19:40:08Z","timestamp":1588966808000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/926512\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":12,"alternative-id":["926512","926512"],"URL":"https:\/\/doi.org\/10.1155\/2013\/926512","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}