{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:46:27Z","timestamp":1777448787219,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2009,11,1]],"date-time":"2009-11-01T00:00:00Z","timestamp":1257033600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2009,11]]},"abstract":"<jats:p>\n                    In this paper, we study the asymptotic behavior of solutions to a chemotaxis model with volume-filling effect subject to the homogeneous Neumann boundary conditions. We establish a non-smooth version of \u0141ojasiewicz\u2013Simon inequality, and we prove that as time goes to infinity the solution to our system converges to an equilibrium in W\n                    <jats:sup>1,p<\/jats:sup>\n                    (\u03a9)\u00d7W\n                    <jats:sup>1,p<\/jats:sup>\n                    (\u03a9), p&gt;max\u2009(n, 2), \u03a9\u2282R\n                    <jats:sup>n<\/jats:sup>\n                    . We also obtain an estimate of the decay rate to equilibrium.\n                  <\/jats:p>","DOI":"10.3233\/asy-2009-0948","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:08:06Z","timestamp":1575054486000},"page":"79-102","source":"Crossref","is-referenced-by-count":15,"title":["On convergence to equilibria for a chemotaxis model with volume-filling effect"],"prefix":"10.1177","volume":"65","author":[{"given":"Jie","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China. E-mails: jiangbryan@gmail.com; yanyanzhangfd@yahoo.cn"}]},{"given":"Yanyan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China. E-mails: jiangbryan@gmail.com; yanyanzhangfd@yahoo.cn"}]}],"member":"179","published-online":{"date-parts":[[2009,11,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2009-0948","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2009-0948","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:38:57Z","timestamp":1777379937000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2009-0948"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2009,11]]}},"alternative-id":["10.3233\/ASY-2009-0948"],"URL":"https:\/\/doi.org\/10.3233\/asy-2009-0948","relation":{"is-cited-by":[{"id-type":"doi","id":"10.1155\/2014\/248657","asserted-by":"object"}]},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11]]}}}