{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T16:18:31Z","timestamp":1787501911137,"version":"3.56.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2014,7,1]],"date-time":"2014-07-01T00:00:00Z","timestamp":1404172800000},"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":[[2014,7]]},"abstract":"<jats:p>We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity\/permeability which models a metal at optical frequency or an ideal negative metamaterial. We highlight an unusual instability phenomenon for this problem when the interface between the two media presents a rounded corner. To establish this result, we provide an asymptotic expansion of the solution, when it is well-defined, in the geometry with a rounded corner. Then, we prove error estimates. Finally, a careful study of the asymptotic expansion allows us to conclude that the solution, when it is well-defined, depends critically on the value of the rounding parameter. We end the paper with a numerical illustration of this instability phenomenon.<\/jats:p>","DOI":"10.3233\/asy-141214","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:33:08Z","timestamp":1575055988000},"page":"43-74","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["A curious instability phenomenon for a rounded corner in presence of a negative material"],"prefix":"10.1177","volume":"88","author":[{"given":"Lucas","family":"Chesnel","sequence":"first","affiliation":[{"name":"Department of Mathematics and Systems Analysis, Aalto University, Aalto, Finland. E-mail: lucas.chesnel@doc.polytechnique.org"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xavier","family":"Claeys","sequence":"additional","affiliation":[{"name":"Laboratory Jacques Louis Lions, University Pierre et Marie Curie, Paris, France. E-mail: claeys@ann.jussieu.fr"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergey A.","family":"Nazarov","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia. E-mail: srgnazarov@yahoo.co.uk"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2014,7,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141214","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141214","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:08Z","timestamp":1777380008000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-141214"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["10.3233\/ASY-141214"],"URL":"https:\/\/doi.org\/10.3233\/asy-141214","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7]]}}}