{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:44:27Z","timestamp":1777448667140,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2008,4,1]],"date-time":"2008-04-01T00:00:00Z","timestamp":1207008000000},"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":[[2008,4]]},"abstract":"<jats:p>\n                    We study asymptotic behavior of global positive solutions of the Cauchy problem for the semilinear parabolic equation u\n                    <jats:sub>t<\/jats:sub>\n                    =\u0394u+u\n                    <jats:sup>p<\/jats:sup>\n                    in R\n                    <jats:sup>N<\/jats:sup>\n                    , where p&gt;1+2\/N, p(N-2)\u2264N+2. The initial data are of the form u(x, 0)=\u03b1\u03d5(x), where \u03d5 is a fixed function with suitable decay at |x|=\u221e and \u03b1&gt;0 is a parameter. There exists a threshold parameter \u03b1\n                    <jats:sup>*<\/jats:sup>\n                    such that the solution exists globally if and only if \u03b1\u2264\u03b1\n                    <jats:sup>*<\/jats:sup>\n                    . Our main results describe the asymptotic behavior of the solutions for \u03b1\u2208(0, \u03b1\n                    <jats:sup>*<\/jats:sup>\n                    ] and in particular exhibit the difference between the behavior of sub-threshold solutions (\u03b1&lt;\u03b1\n                    <jats:sup>*<\/jats:sup>\n                    ) and the threshold solution (\u03b1=\u03b1\n                    <jats:sup>*<\/jats:sup>\n                    ).\n                  <\/jats:p>","DOI":"10.3233\/asy-2008-0872","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:01:02Z","timestamp":1575054062000},"page":"125-141","source":"Crossref","is-referenced-by-count":2,"title":["Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation"],"prefix":"10.1177","volume":"57","author":[{"given":"Peter","family":"Pol\u00e1\u010dik","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pavol","family":"Quittner","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Comenius University, Mlynsk\u00e1 dolina, 84248 Bratislava, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2008,4,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0872","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0872","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:38:34Z","timestamp":1777379914000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2008-0872"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2008,4]]}},"alternative-id":["10.3233\/ASY-2008-0872"],"URL":"https:\/\/doi.org\/10.3233\/asy-2008-0872","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,4]]}}}