{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:52:30Z","timestamp":1777449150101,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2014,9,1]],"date-time":"2014-09-01T00:00:00Z","timestamp":1409529600000},"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":[[2014,9]]},"abstract":"<jats:p>\n                    We consider the stationary diffusion equation in a periodic composite medium made of two components M\n                    <jats:sub>\u03b5<\/jats:sub>\n                    and B\n                    <jats:sub>\u03b5<\/jats:sub>\n                    having very different diffusivity, the ratio between the coefficients of the diffusion in that structure being 1\/\u03b1\n                    <jats:sub>\u03b5<\/jats:sub>\n                    <jats:sup>2<\/jats:sup>\n                    , where \u03b5 is the size of the period and \u03b1\n                    <jats:sub>\u03b5<\/jats:sub>\n                    which represents the amplitude of the diffusion in the inclusions B\n                    <jats:sub>\u03b5<\/jats:sub>\n                    is a decreasing sequence towards zero. We show that the inclusions B\n                    <jats:sub>\u03b5<\/jats:sub>\n                    work on the macroscopic diffusion as holes. In particular for scalings 0&lt;\u03b1\n                    <jats:sub>\u03b5<\/jats:sub>\n                    \ufffd\u03b5 corresponding to very weak diffusion in B\n                    <jats:sub>\u03b5<\/jats:sub>\n                    , the volume fraction of the material at the limit is the well known one in the case of holes.\n                  <\/jats:p>","DOI":"10.3233\/asy-141241","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:34:30Z","timestamp":1575056070000},"page":"173-187","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Diffusion through a composite structure with a high contrasting diffusivity"],"prefix":"10.1177","volume":"89","author":[{"given":"Ali","family":"Sili","sequence":"first","affiliation":[{"name":"Institut de Math\u00e9matiques de Marseille (I2M, UMR 7373), Centre de Math\u00e9matiques et Informatique, 39 rue Joliot-Curie, 13453 Marseille cedex 13, France and D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Toulon, 83957, La Garde cedex, France. E-mail: sili@univ-tln.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,9,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141241","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141241","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:11Z","timestamp":1777380011000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-141241"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["10.3233\/ASY-141241"],"URL":"https:\/\/doi.org\/10.3233\/asy-141241","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9]]}}}