{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:36:10Z","timestamp":1787236570650,"version":"build-2736575974"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\\mathbb{R}^n$, $n\\in\\{1,2,3\\}$. Standard homogenization theory provides, for the limit of a small periodicity length $\\varepsilon&gt;0$, an effective second order wave equation that describes solutions on time intervals $[0,T]$. In order to approximate solutions on large time intervals $[0,T\\varepsilon^{-2}]$, one has to use a dispersive, higher order wave equation. In this work, we provide a well-posed, weakly dispersive effective equation and an estimate for errors between the solution of the original heterogeneous problem and the solution of the dispersive wave equation. We use Bloch-wave analysis to identify a family of relevant limit models and introduce an approach to select a well-posed effective model under symmetry assumptions on the periodic structure. The analytical results are confirmed and illustrated by numerical tests.<\/jats:p>","DOI":"10.1137\/130935033","type":"journal-article","created":{"date-parts":[[2014,4,10]],"date-time":"2014-04-10T11:36:09Z","timestamp":1397129769000},"page":"488-513","source":"Crossref","is-referenced-by-count":36,"title":["Bloch-Wave Homogenization on Large Time Scales and Dispersive Effective Wave Equations"],"prefix":"10.1137","volume":"12","author":[{"given":"T.","family":"Dohnal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Lamacz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"B.","family":"Schweizer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,4,10]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2013.06.002"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/0523084"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.5802\/afst.1055"},{"key":"atypb4","first-page":"65","author":"Allaire G.","year":"1998","journal-title":"Paris"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10231-008-0089-y"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-011-0452-9"},{"key":"atypb7","first-page":"197","volume":"71","author":"Brahim-Otsmane S.","year":"1992","journal-title":"J. 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Lamacz,\n                      Waves in Heterogeneous Media: Long Time Behavior and Dispersive Models\n                      , Ph.D. thesis, TU Dortmund, Dortmund, Germany, 2011."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2000109"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202501001331"},{"key":"atypb25","unstructured":"M. Reed and B. Simon,\n                      Methods of Modern Mathematical Physics. \\textupIV. Analysis of Operators\n                      , Academic Press, New York, 1978."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/0375\u20109601(86)90170\u20102"},{"key":"atypb27","unstructured":"E. Sa\u0301nchez-Palencia,\n                      Nonhomogeneous Media and Vibration Theory\n                      , Lecture Notes in Physics 127, Springer-Verlag, Berlin, 1980."},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1137\/0151049"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/s00161-009-0094-4"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1142\/S1756973710000291"},{"key":"atypb31","doi-asserted-by":"publisher","unstructured":"B. Schweizer and M. Veneroni,\n                      Homogenization of plasticity equations with two-scale convergence methods\n                      , Appl. Anal., to appear. DOI: 10.1080\/00036811.2014.896992.","DOI":"10.1080\/00036811.2014.896992"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1007\/BF02790171"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130935033","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:38:24Z","timestamp":1787233104000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130935033"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1137\/130935033"],"URL":"https:\/\/doi.org\/10.1137\/130935033","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}