{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:55:47Z","timestamp":1777449347007,"version":"3.51.4"},"reference-count":57,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T00:00:00Z","timestamp":1462233600000},"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":[[2016,5,3]]},"abstract":"<jats:p>We consider a system of reaction\u2013diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches the steady state in an asymptotically exponentially long time interval as the viscosity coefficient [Formula: see text] goes to zero. To rigorous describe such behavior, we analyze the dynamics of layered solutions localized far from the stable configurations of the system, and we derive an ODE for the position of the internal interfaces.<\/jats:p>","DOI":"10.3233\/asy-161364","type":"journal-article","created":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T16:45:22Z","timestamp":1462293922000},"page":"131-154","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Slow dynamics in reaction\u2013diffusion systems"],"prefix":"10.1177","volume":"98","author":[{"given":"Marta","family":"Strani","sequence":"first","affiliation":[{"name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche, Universit\u00e9 Paris-Diderot, Paris, France. E-mails:\u00a0,\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,5,3]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1007\/s005260050071"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1993.42.42028"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2008.57.3181"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.0046"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(91)90163-4"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0001-6160(79)90196-2"},{"key":"ref007","first-page":"79","volume":"390","author":"Angenent S.","year":"1988","journal-title":"J. Reine Angew. Math."},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(87)90147-1"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0070595"},{"key":"ref010","unstructured":"S.\u00a0Bartels, A lower bound for the spectrum of the linearized Allen\u2013Cahn operator near a singularity, Bonn, 2010."},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.4171\/ifb\/45"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-008-0151-3"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2010.07.027"},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2013.33.67"},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160430804"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/38.3.195"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500031425"},{"key":"ref018","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160420502"},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(92)90146-E"},{"key":"ref020","doi-asserted-by":"publisher","DOI":"10.1080\/03605309408821057"},{"key":"ref021","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.05.017"},{"key":"ref022","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500013652"},{"key":"ref023","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500031486"},{"key":"ref024","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160450903"},{"key":"ref025","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(74)90088-6"},{"key":"ref026","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(76)90218-3"},{"key":"ref027","doi-asserted-by":"publisher","DOI":"10.1063\/1.432246"},{"key":"ref028","doi-asserted-by":"publisher","DOI":"10.1016\/S1874-575X(02)80034-0"},{"key":"ref029","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(88)90010-7"},{"key":"ref030","doi-asserted-by":"crossref","unstructured":"G.\u00a0Fusco, A geometric approach to the dynamics of\n                      u\n                      \n                        t\n                      \n                      =\n                      \u03b5\n                      2\n                      u\n                      \n                        xx\n                      \n                      +\n                      f\n                      (\n                      u\n                      ) for small\n                      \u03b5\n                      , in: Problems Involving Change of Type, Stuttgart, 1988, Lecture Notes in Physics, Vol.\u00a0359, Springer, Berlin, 1990, pp.\u00a053\u201373.","DOI":"10.1007\/3-540-52595-5_85"},{"key":"ref031","doi-asserted-by":"publisher","DOI":"10.1007\/BF01048791"},{"key":"ref032","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141092226053"},{"key":"ref033","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-85729-112-7"},{"key":"ref034","doi-asserted-by":"publisher","DOI":"10.1080\/03605309608821239"},{"key":"ref035","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(99)00245-X"},{"key":"ref036","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-66282-9"},{"key":"ref037","doi-asserted-by":"publisher","DOI":"10.1137\/0139043"},{"key":"ref038","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(86)90026-7"},{"key":"ref039","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-007-0073-5"},{"key":"ref040","doi-asserted-by":"publisher","DOI":"10.4310\/MAA.1994.v1.n4.a7"},{"key":"ref041","doi-asserted-by":"publisher","DOI":"10.1137\/S003613999326928X"},{"key":"ref042","doi-asserted-by":"publisher","DOI":"10.1137\/120875119"},{"key":"ref043","doi-asserted-by":"publisher","DOI":"10.1016\/0022-5193(78)90332-6"},{"key":"ref044","doi-asserted-by":"publisher","DOI":"10.1137\/0511057"},{"key":"ref045","doi-asserted-by":"publisher","DOI":"10.1137\/0518124"},{"key":"ref046","doi-asserted-by":"publisher","DOI":"10.1063\/1.431776"},{"key":"ref047","first-page":"489","volume":"20","author":"Ostrovskii A.","year":"1975","journal-title":"Biofizika"},{"key":"ref048","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2007.03.007"},{"key":"ref049","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1989.0027"},{"key":"ref050","unstructured":"M.\u00a0Reed and B.\u00a0Simon, Methods of Modern Mathematical Physics. II: Fourier Analysis, Self-Adjointness, Academic Press, New York, 1975."},{"key":"ref051","unstructured":"M.\u00a0Reed and B.\u00a0Simon, Methods of Modern Mathematical Physics. IV: Analysis of Operators, Academic Press, New York, 1978."},{"key":"ref052","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160480202"},{"key":"ref053","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2006.12.005"},{"key":"ref054","doi-asserted-by":"publisher","DOI":"10.1216\/rmjm\/1181072968"},{"key":"ref055","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-014-9418-6"},{"key":"ref056","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/28\/12\/4331"},{"key":"ref057","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792598003623"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-161364","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-161364","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-161364","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:48Z","timestamp":1777380048000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-161364"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,3]]},"references-count":57,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2016,5,3]]}},"alternative-id":["10.3233\/ASY-161364"],"URL":"https:\/\/doi.org\/10.3233\/asy-161364","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,3]]}}}