{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:44:55Z","timestamp":1777448695801,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2008,7,1]],"date-time":"2008-07-01T00:00:00Z","timestamp":1214870400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2008,7]]},"abstract":"<jats:p>Second initial boundary problem in narrow domains of width \u03b5\ufffd1 for linear second-order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution of such a problem converges as \u03b5\u21930 to the solution of a standard reaction\u2013diffusion equation in a domain of reduced dimension. This reduction allows to obtain some results concerning wave front propagation in narrow domains. In particular, we describe conditions leading to jumps of the wave front.<\/jats:p>","DOI":"10.3233\/asy-2008-0894","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:02:51Z","timestamp":1575054171000},"page":"227-249","source":"Crossref","is-referenced-by-count":6,"title":["Reaction\u2013diffusion equations with nonlinear boundary conditions in narrow domains"],"prefix":"10.1177","volume":"59","author":[{"given":"Mark","family":"Freidlin","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Maryland, College Park, MD 20742, USA. E-mails: {mif, kspiliop}@math.umd.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantinos","family":"Spiliopoulos","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Maryland, College Park, MD 20742, USA. E-mails: {mif, kspiliop}@math.umd.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2008,7,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0894","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0894","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:38:40Z","timestamp":1777379920000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2008-0894"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["10.3233\/ASY-2008-0894"],"URL":"https:\/\/doi.org\/10.3233\/asy-2008-0894","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7]]}}}