{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:32:52Z","timestamp":1777447972300,"version":"3.51.4"},"reference-count":37,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T00:00:00Z","timestamp":1565568000000},"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":[[2019,8,12]]},"abstract":"<jats:p>We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of the Laplace equation with the same dynamical boundary condition as the diffusion coefficient tends to infinity.<\/jats:p>","DOI":"10.3233\/asy-181517","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T11:27:37Z","timestamp":1565695657000},"page":"37-57","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition"],"prefix":"10.1177","volume":"114","author":[{"given":"Marek","family":"Fila","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava, Slovakia. E-mails:\u00a0,\u00a0"}]},{"given":"Kazuhiro","family":"Ishige","sequence":"additional","affiliation":[{"name":"Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan. E-mail:\u00a0"}]},{"given":"Tatsuki","family":"Kawakami","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Informatics, Ryukoku University, Seta Otsu 520-2194, Japan. E-mail:\u00a0"}]},{"given":"Johannes","family":"Lankeit","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava, Slovakia. E-mails:\u00a0,\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2019,8,12]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.57262\/die\/1356123007"},{"issue":"1","key":"ref002","first-page":"35","volume":"17","author":"Bandle C.","year":"2006","journal-title":"Atti Accad Naz Lincei Rend Lincei Mat Appl."},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02571805"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1080\/03605309308820976"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.57262\/die\/1369083468"},{"issue":"4","key":"ref006","first-page":"325","volume":"20","author":"Escher J.","year":"2000","journal-title":"Analysis (Munich)"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2012.11.1285"},{"issue":"1","key":"ref008","first-page":"69","volume":"18","author":"Fila M.","year":"2013","journal-title":"Adv Differential Equations."},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-015-0856-8"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2015.11.014"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1007\/s13163-017-0225-6"},{"key":"ref012","unstructured":"M.\u00a0Fila, K.\u00a0Ishige and T.\u00a0Kawakami, The large diffusion limit for the heat equation with a dynamical boundary condition, 2018 June, preprint arXiv:1806.06308."},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1007\/PL00004770"},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1476(199710)20:15<1325::AID-MMA916>3.0.CO;2-G"},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8765-6_12"},{"issue":"11","key":"ref016","first-page":"5015","volume":"33","author":"Fiscella A.","year":"2013","journal-title":"Discrete Contin Dyn Syst."},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2012.02.010"},{"key":"ref018","doi-asserted-by":"publisher","DOI":"10.1007\/s00032-015-0242-1"},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/pdt057"},{"key":"ref020","doi-asserted-by":"publisher","DOI":"10.1090\/S0033-569X-2015-01363-5"},{"key":"ref021","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-018-0542-6"},{"key":"ref022","first-page":"1:45","volume":"1117","author":"Giga Y.","year":"2018","journal-title":"Hokkaido Univ Preprint Series in Math."},{"key":"ref023","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500023945"},{"key":"ref024","doi-asserted-by":"publisher","DOI":"10.14492\/hokmj\/1381413677"},{"issue":"2","key":"ref025","first-page":"9","volume":"22","author":"Kirane M.","year":"2004","journal-title":"Bol Soc Parana Mat (3)"},{"issue":"6","key":"ref026","first-page":"768","volume":"38","author":"Kirane M.","year":"2002","journal-title":"Differ Uravn"},{"key":"ref027","unstructured":"J.L.\u00a0Lions, Quelques M\u00e9thodes de R\u00e9solution des Probl\u00e8mes aux Limites Non Lin\u00e9aires, Dunod; Gauthier-Villars, Paris, 1969."},{"key":"ref028","doi-asserted-by":"publisher","DOI":"10.1007\/s10231-013-0329-7"},{"key":"ref029","doi-asserted-by":"publisher","DOI":"10.1080\/03605300801970960"},{"key":"ref030","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500003838"},{"key":"ref031","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611506015875"},{"issue":"5","key":"ref032","first-page":"467","volume":"5","author":"von Below J.","year":"2000","journal-title":"J\u00a0Inequal Appl."},{"key":"ref033","doi-asserted-by":"publisher","DOI":"10.1081\/PDE-120019380"},{"key":"ref034","unstructured":"J.\u00a0von Below and G.\u00a0Pincet Mailly, Blow up for some nonlinear parabolic problems with convection under dynamical boundary conditions. Discrete Contin Dyn Syst. 2007; (Dynamical systems and differential equations. Proceedings of the 6th AIMS International Conference, suppl.): 1031\u20131041."},{"issue":"3","key":"ref035","first-page":"825","volume":"6","author":"von Below J.","year":"2013","journal-title":"Discrete Contin Dyn Syst Ser S."},{"issue":"1","key":"ref036","first-page":"67","volume":"17","author":"Wu H.","year":"2007","journal-title":"Adv Math Sci Appl."},{"key":"ref037","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-003-0104-x"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181517","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-181517","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181517","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:36:27Z","timestamp":1777379787000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-181517"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,12]]},"references-count":37,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,8,12]]}},"alternative-id":["10.3233\/ASY-181517"],"URL":"https:\/\/doi.org\/10.3233\/asy-181517","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,12]]}}}