{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:52:05Z","timestamp":1777449125184,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2014,6,1]],"date-time":"2014-06-01T00:00:00Z","timestamp":1401580800000},"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":[[2014,6]]},"abstract":"<jats:p>Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.<\/jats:p>","DOI":"10.3233\/asy-131208","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:32:41Z","timestamp":1575055961000},"page":"191-221","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":15,"title":["Smooth attractors for the quintic wave equations with fractional damping"],"prefix":"10.1177","volume":"87","author":[{"given":"Anton","family":"Savostianov","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK. E-mails: {a.savostianov, s.zelik}@surrey.ac.uk"}]},{"given":"Sergey","family":"Zelik","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK. E-mails: {a.savostianov, s.zelik}@surrey.ac.uk"}]}],"member":"179","published-online":{"date-parts":[[2014,6,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131208","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131208","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:07Z","timestamp":1777380007000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-131208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.3233\/ASY-131208"],"URL":"https:\/\/doi.org\/10.3233\/asy-131208","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}