{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T15:42:00Z","timestamp":1781797320055,"version":"3.54.5"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2012,8,1]],"date-time":"2012-08-01T00:00:00Z","timestamp":1343779200000},"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":[[2012,8]]},"abstract":"<jats:p>We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non-local evolution one having a travelling wave solution with zero speed of propagation with exactly the same profile as the original one. This procedure allows us to compute simultaneously the travelling wave profile and its propagation speed avoiding moving meshes, as we illustrate with several numerical examples. We analyze the relation of the new equation with the original one in the entire real line. We also analyze the behavior of the non-local problem in a bounded interval with appropriate boundary conditions. We show that it has a unique stationary solution which approaches the traveling wave as the interval gets larger and larger and that is asymptotically stable for large enough intervals.<\/jats:p>","DOI":"10.3233\/asy-2011-1088","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:21:37Z","timestamp":1575055297000},"page":"145-186","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Approximating travelling waves by equilibria of non-local equations"],"prefix":"10.1177","volume":"78","author":[{"given":"Jose M.","family":"Arrieta","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Universidad Complutense de Madrid, Madrid, Spain. E-mail: arrieta@mat.ucm.es"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mar\u00eda","family":"L\u00f3pez-Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik. Universit\u00e4t Z\u00fcrich, Z\u00fcrich, Switzertland. E-mail: maria.lopez@math.uzh.ch"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Enrique","family":"Zuazua","sequence":"additional","affiliation":[{"name":"Basque Center for Applied Mathematics, Bizkaia Technology Park, Derio, Basque Country, Spain. E-mail: zuazua@bcamath.org"},{"name":"Ikerbasque \u2013 Basque Foundation for Science, Bilbao, Basque Country, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2012,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1088","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1088","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:31Z","timestamp":1777379971000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2011-1088"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["10.3233\/ASY-2011-1088"],"URL":"https:\/\/doi.org\/10.3233\/asy-2011-1088","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8]]}}}