{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:52:23Z","timestamp":1777449143748,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T00:00:00Z","timestamp":1406851200000},"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":[[2014,8]]},"abstract":"<jats:p>In Quart. Appl. Math. 71 (2013), 183\u2013199, the authors find sharp exponential rates for the energy decay of nontrivial solutions to the abstract telegraph equation<\/jats:p>\n                  <jats:p>\n                    u\n                    <jats:sub>tt<\/jats:sub>\n                    +2au\n                    <jats:sub>t<\/jats:sub>\n                    +S\n                    <jats:sup>2<\/jats:sup>\n                    u=0,\n                  <\/jats:p>\n                  <jats:p>where S is a strictly positive self-adjoint operator in a (complex) Hilbert space and a is a positive constant. The aim of this paper is a further extension of these results by considering equations of the form<\/jats:p>\n                  <jats:p>\n                    u\n                    <jats:sub>tt<\/jats:sub>\n                    +2F(S)u\n                    <jats:sub>t<\/jats:sub>\n                    +S\n                    <jats:sup>2<\/jats:sup>\n                    u=0,\n                  <\/jats:p>\n                  <jats:p>where the damping term involves the action of the positive self-adjoint operator F(S). The main assumption on the continuous function F\u2009:(0,+\u221e)\u2192(0,+\u221e) is that g(x)=F(x)\u2212x changes sign only once, being positive close to zero. We obtain sharp estimates of the form<\/jats:p>\n                  <jats:p>\n                    E(t)\u2264Ce\n                    <jats:sup>\u22122\u03b1t<\/jats:sup>\n                    ,\n                  <\/jats:p>\n                  <jats:p>where \u03b1&gt;0 depends on the relative position of the bottom of the spectrum of S and the point where g vanishes, as well as on the specific behavior of F on the spectrum of S. The general result is then applied to some particular classes of functions F. We also provide a number of applications.<\/jats:p>","DOI":"10.3233\/asy-141222","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:33:48Z","timestamp":1575056028000},"page":"217-232","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Overdamping and energy decay for abstract wave equations with strong damping"],"prefix":"10.1177","volume":"88","author":[{"given":"Gis\u00e8le Ruiz","family":"Goldstein","sequence":"first","affiliation":[{"name":"University of Memphis, Memphis, TN, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jerome A.","family":"Goldstein","sequence":"additional","affiliation":[{"name":"University of Memphis, Memphis, TN, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillermo","family":"Reyes","sequence":"additional","affiliation":[{"name":"University of California, Irvine, Irvine, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141222","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141222","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:09Z","timestamp":1777380009000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-141222"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.3233\/ASY-141222"],"URL":"https:\/\/doi.org\/10.3233\/asy-141222","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}