{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T11:15:38Z","timestamp":1761218138338,"version":"3.38.0"},"reference-count":18,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2019,3,6]],"date-time":"2019-03-06T00:00:00Z","timestamp":1551830400000},"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":[[2019,3,6]]},"abstract":"<jats:p> We perform the asymptotic analysis of the scalar advection-diffusion equation [Formula: see text], [Formula: see text], [Formula: see text], with respect to the diffusion coefficient \u03b5. We use the matched asymptotic expansion method which allows to describe the boundary layers of the solution. We then use the asymptotics to discuss the controllability property of the solution for [Formula: see text]. <\/jats:p>","DOI":"10.3233\/asy-181497","type":"journal-article","created":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T15:36:32Z","timestamp":1552059392000},"page":"59-106","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Asymptotic analysis of an advection-diffusion equation and application to boundary controllability"],"prefix":"10.1177","volume":"112","author":[{"given":"Youcef","family":"Amirat","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Blaise Pascal, Universit\u00e9 Clermont Auvergne, UMR CNRS 6620, Campus universitaire des C\u00e9zeaux, 3, place Vasarely, 63178, Aubi\u00e8re, France. E-mails:\u00a0,\u00a0"}]},{"given":"Arnaud","family":"M\u00fcnch","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Blaise Pascal, Universit\u00e9 Clermont Auvergne, UMR CNRS 6620, Campus universitaire des C\u00e9zeaux, 3, place Vasarely, 63178, Aubi\u00e8re, France. E-mails:\u00a0,\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2019,3,6]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-70914-7"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-2005-707"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1137\/140961146"},{"key":"ref004","unstructured":"A.V.\u00a0Fursikov and O.Y.\u00a0Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series, Seoul National University Research Institute of Mathematics, Vol.\u00a034, Global Analysis Research Center, Seoul, 1996."},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2009.06.035"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1080\/03605300701743756"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3968-0"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8134-0"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1080\/03605309508821097"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0060528"},{"key":"ref011","unstructured":"J.L.\u00a0Lions, Contr\u00f4labilit\u00e9 Exacte, Perturbations et Stabilisation de Syst\u00e8mes Distribu\u00e9s. Tome 2, Recherches en Math\u00e9matiques Appliqu\u00e9es [Research in Applied Mathematics], Vol.\u00a09, Masson, Paris, 1988, Perturbations. [Perturbations]."},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2012.06.004"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2015.06.031"},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2013.11.013"},{"key":"ref015","doi-asserted-by":"crossref","unstructured":"A.\u00a0M\u00fcnch, Numerical estimation of the cost of boundary controls for the equation yt\u2212\u03b5yxx+Myx=0 with respect to \u03b5, SEMA-SIMAI Springer series \u2013 Recent Advances in PDEs: Analysis, Numerics and controls, 2018, in honor of Prof. Enrique Fernandez-Cara\u2019s 60 birthday, 17.","DOI":"10.1007\/978-3-319-97613-6_9"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2013.02.001"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-73782-4"},{"key":"ref018","unstructured":"M.\u00a0Van Dyke, Perturbation Methods in Fluid Mechanics, annotated edn, The Parabolic Press, Stanford, Calif., 1975."}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181497","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-181497","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181497","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T13:43:39Z","timestamp":1741614219000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-181497"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,6]]},"references-count":18,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,3,6]]}},"alternative-id":["10.3233\/ASY-181497"],"URL":"https:\/\/doi.org\/10.3233\/asy-181497","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"type":"print","value":"0921-7134"},{"type":"electronic","value":"1875-8576"}],"subject":[],"published":{"date-parts":[[2019,3,6]]}}}