{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:35:14Z","timestamp":1772285714227,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2007,7,12]],"date-time":"2007-07-12T00:00:00Z","timestamp":1184198400000},"content-version":"unspecified","delay-in-days":467,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[2006,4]]},"abstract":"<jats:p>In this article we study the behaviour of a heterogeneous thin film whose microstructure oscillates on a scale that is comparable to that of the thickness of the domain. The argument is based on a three-dimensional\u2013two-dimensional reduction through a \u0393-convergence analysis, techniques of two-scale convergence and a decoupling procedure between the oscillating variable and the in-plane variable.<\/jats:p>","DOI":"10.1017\/s0308210500004534","type":"journal-article","created":{"date-parts":[[2007,7,16]],"date-time":"2007-07-16T10:48:36Z","timestamp":1184582916000},"page":"223-243","source":"Crossref","is-referenced-by-count":13,"title":["3D\u20132D analysis of a thin film with periodic microstructure"],"prefix":"10.1017","volume":"136","author":[{"given":"Jean-Fran\u00e7ois","family":"Babadjian","sequence":"first","affiliation":[]},{"given":"Margarida","family":"Ba\u00eda","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2007,7,12]]},"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210500004534","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,6]],"date-time":"2019-04-06T19:46:58Z","timestamp":1554580018000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210500004534\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,4]]}},"alternative-id":["S0308210500004534"],"URL":"https:\/\/doi.org\/10.1017\/s0308210500004534","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,4]]}}}