{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T22:23:33Z","timestamp":1778538213153,"version":"3.51.4"},"reference-count":27,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T00:00:00Z","timestamp":1565568000000},"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":[[2019,8,12]]},"abstract":"<jats:p>In this report we obtain higher order asymptotic expansions of solutions to wave equations with frictional and viscoelastic damping terms. Although the diffusion phenomena are dominant, differences between the solutions we deal with and those of heat equations can be seen by comparing the second order expansions of them. In order to analyze such effects we consider the weighted [Formula: see text] initial data. We also give some lower bounds which show the optimality of obtained expansions.<\/jats:p>","DOI":"10.3233\/asy-181516","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T11:27:31Z","timestamp":1565695651000},"page":"19-36","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms"],"prefix":"10.1177","volume":"114","author":[{"given":"Ryo","family":"Ikehata","sequence":"first","affiliation":[{"name":"Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan. E-mail:\u00a0"}]},{"given":"Hironori","family":"Michihisa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan. E-mail:\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2019,8,12]]},"reference":[{"key":"ref001","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00030-016-0428-4","volume":"24","author":"D\u2019Abbicco M.","year":"2017","journal-title":"Nonlinear Differ. Equ. Appl."},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1002\/mma.2913"},{"key":"ref003","first-page":"153","volume":"63","author":"Duoandikoetxea J.","year":"1992","journal-title":"C. R. Acad. Sci. Paris Ser. I Math."},{"key":"ref004","unstructured":"T.\u00a0Hosono, Asymptotic behavior of solutions for nonlinear partial differential equations with dissipation, Doctoral thesis, Kyushu University, 2006."},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.03.034"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1002\/mma.476"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2014.05.031"},{"key":"ref008","first-page":"939","volume":"25","author":"Ikehata R.","year":"2012","journal-title":"Diff. Int. Eqns"},{"key":"ref009","first-page":"505","volume":"30","author":"Ikehata R.","year":"2017","journal-title":"Diff. Int. Eqns"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-161361"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2016.10.008"},{"key":"ref012","unstructured":"R.\u00a0Ikehata and H.\u00a0Takeda, Asymptotic profiles of solutions for structural damped wave equations, submitted, 2016, arXiv:1607.01839."},{"key":"ref013","unstructured":"R.\u00a0Ikehata and H.\u00a0Takeda, Large time behavior of global solutions to nonlinear wave equations with frictional and viscoelastic damping terms, to appear in\n                      Osaka J. Math."},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2013.01.023"},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1137\/16M1101428"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.4064\/sm-143-2-175-197"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0396(03)00026-3"},{"key":"ref018","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195190962"},{"key":"ref019","unstructured":"H.\u00a0Michihisa, Expanding methods for evolution operators of strongly damped wave equations, preprint, 2018."},{"key":"ref020","unstructured":"H.\u00a0Michihisa, L2 asymptotic profiles of solutions to linear damped wave equations, preprint, 2017, arXiv:1710.04870."},{"key":"ref021","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/1191418647"},{"key":"ref022","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-003-0516-0"},{"key":"ref023","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202501001331"},{"key":"ref024","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(85)90001-X"},{"key":"ref025","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-016-1735-5"},{"key":"ref026","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1476(200002)23:3<203::AID-MMA111>3.0.CO;2-M"},{"key":"ref027","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-151295"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181516","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-181516","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181516","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:36:27Z","timestamp":1777379787000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-181516"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,12]]},"references-count":27,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,8,12]]}},"alternative-id":["10.3233\/ASY-181516"],"URL":"https:\/\/doi.org\/10.3233\/asy-181516","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,12]]}}}