{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:47:54Z","timestamp":1777448874656,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2010,12,1]],"date-time":"2010-12-01T00:00:00Z","timestamp":1291161600000},"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":[[2010,12]]},"abstract":"<jats:p>\n                    This paper studies heat equations with weighted nonlinear absorptions of the form u\n                    <jats:sub>t<\/jats:sub>\n                    =u\n                    <jats:sub>xx<\/jats:sub>\n                    \u2212Mf(x)u\n                    <jats:sup>\u2212p<\/jats:sup>\n                    in (\u22121,1)\u00d7(0,T) subject to Dirichlet boundary conditions u(\u22121,t)=u(1,t)=1 and initial data \u03d5(x). The asymptotic estimates to quenching time and set of solutions as M\u2192+\u221e is established by local energy estimates. It is obtained that the quenching time T~m\/(p+1)\u00b7M\n                    <jats:sup>\u22121<\/jats:sup>\n                    with m=(max\u2009\n                    <jats:sub>x<\/jats:sub>\n                    (f(x)\/\u03d5\n                    <jats:sup>p+1<\/jats:sup>\n                    (x)))\n                    <jats:sup>\u22121<\/jats:sup>\n                    as M\u2192+\u221e. It is shown also how the quenching set concentrates near the maximum points of f\/\u03d5\n                    <jats:sup>p+1<\/jats:sup>\n                    for large M.\n                  <\/jats:p>","DOI":"10.3233\/asy-2010-1006","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:14:05Z","timestamp":1575054845000},"page":"125-139","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotic estimates to quenching solutions of heat equations with weighted absorptions"],"prefix":"10.1177","volume":"70","author":[{"given":"Wei","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China"}]},{"given":"Sining","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China"}]}],"member":"179","published-online":{"date-parts":[[2010,12,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-1006","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-1006","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:14Z","timestamp":1777379954000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2010-1006"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["10.3233\/ASY-2010-1006"],"URL":"https:\/\/doi.org\/10.3233\/asy-2010-1006","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}