{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:50:43Z","timestamp":1753883443589,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,4,14]],"date-time":"2011-04-14T00:00:00Z","timestamp":1302739200000},"content-version":"vor","delay-in-days":103,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Vietnam's National Foundation for Science and Technology Development","award":["101.01-2010.05"],"award-info":[{"award-number":["101.01-2010.05"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We study the long\u2010time behavior of solutions to nonautonomous semilinear parabolic systems involving the Grushin operators in bounded domains. We prove the existence of a pullback <jats:italic>\ud835\udc9f<\/jats:italic>\u2010attractor in \n\t\t\t\t(<jats:italic>L<\/jats:italic><jats:sup>2<\/jats:sup>(\u03a9))\u2009<jats:sup><jats:italic>m<\/jats:italic><\/jats:sup> for the corresponding process in the general case. When the system has a special gradient structure, we prove that the obtained pullback \n\t\t\t\t<jats:italic>\ud835\udc9f<\/jats:italic>\u2010attractor is more regular and has a finite fractal dimension. The obtained results, in particular, extend and improve some existing ones for the reaction\u2010diffusion equations and the Grushin equations.<\/jats:p>","DOI":"10.1155\/2011\/178057","type":"journal-article","created":{"date-parts":[[2011,4,14]],"date-time":"2011-04-14T19:33:26Z","timestamp":1302809606000},"update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Dynamics of Nonautonomous Parabolic Systems Involving the Grushin Operators"],"prefix":"10.1155","volume":"2011","author":[{"given":"Anh","family":"Cung The","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toi","family":"Vu Manh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,4,14]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.03.111"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.07.027"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.11.187"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.10.065"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.02.041"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1080\/14689360701611821"},{"key":"e_1_2_6_7_2","first-page":"163","article-title":"A certain class of elliptic pseudodifferential operators that are degenerate on a submanifold","volume":"84","author":"Gru\u0161in V. 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