{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T13:42:58Z","timestamp":1773582178868,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2015,7,23]]},"abstract":"<jats:p>In this paper, we present the 3D-1D asymptotic analysis of the Dirichlet spectral problem associated with an elliptic operator with axial periodic heterogeneities. We extend to the 3D-1D case previous 3D-2D results (see [10]) and we analyze the special case where the scale of thickness is much smaller than the scale of the heterogeneities and the planar coefficient has a unique global minimum in the periodic cell. These results are of great relevance in the comprehension of the wave propagation in nanowires showing axial heterogeneities (see [17]).<\/jats:p>","DOI":"10.4171\/pm\/1967","type":"journal-article","created":{"date-parts":[[2015,7,23]],"date-time":"2015-07-23T17:45:03Z","timestamp":1437673503000},"page":"247-266","source":"Crossref","is-referenced-by-count":6,"title":["Spectral analysis in thin tubes with axial heterogeneities"],"prefix":"10.4171","volume":"72","author":[{"given":"Rita","family":"Ferreira","sequence":"first","affiliation":[{"name":"King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia"}]},{"given":"M. Lu\u00edsa","family":"Mascarenhas","sequence":"additional","affiliation":[{"name":"Universidade Nova de Lisboa, Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9874-6227","authenticated-orcid":false,"given":"Andrey","family":"Piatnitski","sequence":"additional","affiliation":[{"name":"Narvik University College, Norway"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/PM\/1967","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:12:36Z","timestamp":1762261956000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/1967"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,23]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.4171\/pm\/1967","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"value":"0032-5155","type":"print"},{"value":"1662-2758","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,23]]}}}