{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T04:25:18Z","timestamp":1741753518025,"version":"3.38.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2014,7,1]],"date-time":"2014-07-01T00:00:00Z","timestamp":1404172800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2014,7]]},"abstract":"<jats:p> We consider the Cauchy problem for mildly degenerate Kirchhoff type dissipative wave equations: \u03c1u\u2033+\u2016A<jats:sup>1\/2<\/jats:sup>u(t)\u2016<jats:sup>2\u03b3<\/jats:sup>Au+u\u2032=0 in R<jats:sup>N<\/jats:sup>\u00d7R<jats:sup>+<\/jats:sup>, u(x,0)=u<jats:sub>0<\/jats:sub>(x), u\u2032(x,0)=u<jats:sub>1<\/jats:sub>(x) in R<jats:sup>N<\/jats:sup>, with \u03c1&gt;0, \u03b3\u22651, and \u2016A<jats:sup>1\/2<\/jats:sup>u<jats:sub>0<\/jats:sub>\u2016&gt;0. When either the coefficient \u03c1 or the initial data {u<jats:sub>0<\/jats:sub>,u<jats:sub>1<\/jats:sub>} are small, we prove the existence of global solutions by using several identities for energies. Moreover, we derive lower decay estimates of the solutions, and upper decay estimates of their second order derivatives. <\/jats:p>","DOI":"10.3233\/asy-141215","type":"journal-article","created":{"date-parts":[[2019,11,30]],"date-time":"2019-11-30T00:33:10Z","timestamp":1575073990000},"page":"75-92","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Decay estimates of solutions for mildly degenerate Kirchhoff type dissipative wave equations in unbounded domains"],"prefix":"10.1177","volume":"88","author":[{"given":"Kosuke","family":"Ono","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, The University of Tokushima, 1-1 Minamijosanjima-cho, Tokushima 770-8502, Japan. E-mail: ono@ias.tokushima-u.ac.jp"}]}],"member":"179","published-online":{"date-parts":[[2014,7,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141215","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141215","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T08:14:57Z","timestamp":1741680897000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-141215"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["10.3233\/ASY-141215"],"URL":"https:\/\/doi.org\/10.3233\/asy-141215","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"type":"print","value":"0921-7134"},{"type":"electronic","value":"1875-8576"}],"subject":[],"published":{"date-parts":[[2014,7]]}}}