{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:30:07Z","timestamp":1787239807007,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["170544IA"],"award-info":[{"award-number":["170544IA"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bistable cases, we prove the first sharp quantitative estimate on the (sharp) threshold values. Furthermore, numerical explorations allow us to conjecture some refined estimates. Last we provide related results in the case of a degenerate monostable nonlinearity \u201cnot enjoying the hair trigger effect.\u201d<\/jats:p>","DOI":"10.1137\/19m1292187","type":"journal-article","created":{"date-parts":[[2020,5,26]],"date-time":"2020-05-26T12:15:35Z","timestamp":1590495335000},"page":"1291-1311","source":"Crossref","is-referenced-by-count":8,"title":["Quantitative Estimates of the Threshold Phenomena for Propagation in Reaction-Diffusion Equations"],"prefix":"10.1137","volume":"19","author":[{"given":"Matthieu","family":"Alfaro","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arnaud","family":"Ducrot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7390-4295","authenticated-orcid":true,"given":"Gr\u00e9gory","family":"Faye","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,5,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/14150"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"D. G. Aronson and H. F. Weinberger,\n                      Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation\n                      , in Partial Differential Equations and Related Topics, Lecture Notes in Math. 446, Springer, Berlin, 1975.","DOI":"10.1007\/BFb0070595"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(78)90130-5"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/198"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/18M1165797"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00250432"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(89)90086-7"},{"key":"atypb8","first-page":"109","volume":"13","author":"Fujita H.","year":"1966","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. I"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.244101"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1111\/j.1752-4571.2009.00112.x"},{"key":"atypb11","first-page":"398","volume":"65","author":"Kanel' Ja. I.","year":"1964","journal-title":"S.)"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160390403"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/0150083"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-013-0220-7"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2017038"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(96)00203-5"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-010-0316-8"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/0514086"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-05-00504-7"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1292187","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:57:28Z","timestamp":1787237848000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1292187"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/19M1292187"],"URL":"https:\/\/doi.org\/10.1137\/19m1292187","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}