{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:20Z","timestamp":1777447880647,"version":"3.51.4"},"reference-count":24,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2017,6,15]],"date-time":"2017-06-15T00:00:00Z","timestamp":1497484800000},"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":[[2017,6,15]]},"abstract":"<jats:p>The energy of a type II superconductor placed in a strong non-uniform, smooth and signed magnetic field is displayed via a universal reference function defined by means of a simplified two dimensional Ginzburg\u2013Landau functional. We study the asymptotic behavior of this functional in a specific asymptotic regime, thereby linking it to a one dimensional functional, using methods developed by Almog\u2013Helffer and Fournais\u2013Helffer devoted to the analysis of surface superconductivity in the presence of a uniform magnetic field. As a result, we obtain an asymptotic formula reminiscent of the one for the surface superconductivity regime, where the zero set of the magnetic field plays the role of the superconductor\u2019s surface.<\/jats:p>","DOI":"10.3233\/asy-171424","type":"journal-article","created":{"date-parts":[[2017,6,16]],"date-time":"2017-06-16T11:06:45Z","timestamp":1497611205000},"page":"135-163","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Ginzburg\u2013Landau energy with a magnetic field vanishing along a curve"],"prefix":"10.1177","volume":"103","author":[{"given":"Ayman","family":"Kachmar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lebanese University, Nabatieh, Lebanon. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marwa","family":"Nasrallah","sequence":"additional","affiliation":[{"name":"Lebanese International University, Beirut, Lebanon. E-mail:\u00a0"},{"name":"Faculty of Sciences, Section IV, Lebanese University, Bekaa, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,6,15]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1137\/050636796"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-016-1037-4"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2016087"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2013.12.002"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-151286"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2016.02.002"},{"key":"ref007","doi-asserted-by":"crossref","unstructured":"A.\u00a0Contreras and X.\u00a0Lamy, Persistence of superconductivity in thin shells beyond Hc1, Commun. Contemp. 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