{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T21:29:04Z","timestamp":1780090144670,"version":"3.54.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2008,8,1]],"date-time":"2008-08-01T00:00:00Z","timestamp":1217548800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2008,8]]},"abstract":"<jats:p>\n                    We consider the \u0393-limit of a family of functionals which model the interaction of a material that undergoes phase transition with a rapidly oscillating conservative vector field. These functionals consist of a gradient term, a double-well potential and a vector field. The scaling is such that all three terms scale in the same way and the frequency of the vector field is equal to the interface thickness. Difficulties arise from the fact that the two global minimizers of the functionals are nonconstant and converge only in the weak L\n                    <jats:sup>2<\/jats:sup>\n                    -topology.\n                  <\/jats:p>","DOI":"10.3233\/asy-2008-0897","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:03:07Z","timestamp":1575054187000},"page":"29-59","source":"Crossref","is-referenced-by-count":2,"title":["Gradient theory of phase transitions with a rapidly oscillating forcing term"],"prefix":"10.1177","volume":"60","author":[{"given":"Nicolas","family":"Dirr","sequence":"first","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, D-04103 Leipzig, Germany and Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. E-mail: N.Dirr@maths.bath.ac.uk"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcello","family":"Lucia","sequence":"additional","affiliation":[{"name":"Mathematics Department, The City University of New York, CSI, Staten Island, NY 10314, USA. E-mail: mlucia@math.csi.cuny.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matteo","family":"Novaga","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy. E-mail: novaga@dm.unipi.it"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2008,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0897","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0897","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:38:45Z","timestamp":1777379925000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2008-0897"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2008,8]]}},"alternative-id":["10.3233\/ASY-2008-0897"],"URL":"https:\/\/doi.org\/10.3233\/asy-2008-0897","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8]]}}}