{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:45:52Z","timestamp":1777448752257,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"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":[[2009,1]]},"abstract":"<jats:p>\n                    The paper contains results concerning the stability properties of solutions to a simplified Keller\u2013Segel problem modelling chemotaxis in the whole space R\n                    <jats:sup>2<\/jats:sup>\n                    . First, the existence of solutions to considered system is proved, as well as for this system with the elliptic equation replaced by its parabolic version with time derivative multiplied by a positive parameter \u03b5. Secondly, the stability of the model is shown, namely the convergence of solutions of parabolic\u2013parabolic system to a solution of parabolic\u2013elliptic one, when a suitable parameter in the system under consideration converges towards zero.\n                  <\/jats:p>","DOI":"10.3233\/asy-2008-0907","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:03:57Z","timestamp":1575054237000},"page":"35-59","source":"Crossref","is-referenced-by-count":21,"title":["Stability property of the two-dimensional Keller\u2013Segel model"],"prefix":"10.1177","volume":"61","author":[{"given":"Andrzej","family":"Raczy\u0144ski","sequence":"first","affiliation":[{"name":"Instytut Matematyczny, Uniwersytet Wroc\u0142awski, pl. Grunwaldzki 2\/4, 50\u2013384 Wroc\u0142aw, Poland. E-mail: Andrzej.Raczynski@math.uni.wroc.pl"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2009,1,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0907","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0907","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:38:48Z","timestamp":1777379928000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2008-0907"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.3233\/ASY-2008-0907"],"URL":"https:\/\/doi.org\/10.3233\/asy-2008-0907","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}