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dc.contributor.authorBouin, Emeric
dc.contributor.authorHenderson, Christopher
dc.date.accessioned2021-09-02T00:03:34Z
dc.date.available2021-09-02T00:03:34Z
dc.date.issued2021-12
dc.identifier.citationBouin, E., & Henderson, C. (2021). The Bramson delay in a Fisher–KPP equation with log-singular nonlinearity. Nonlinear Analysis, Theory, Methods and Applications, 213.en_US
dc.identifier.issn0362-546X
dc.identifier.doi10.1016/j.na.2021.112508
dc.identifier.urihttp://hdl.handle.net/10150/661350
dc.description.abstractWe consider a class of reaction–diffusion equations of Fisher–KPP type in which the nonlinearity (reaction term) f is merely C1 at u=0 due to a logarithmic competition term. We first derive the asymptotic behavior of (minimal speed) traveling wave solutions that is, we obtain precise estimates on the decay to zero of the traveling wave profile at infinity. We then use this to characterize the Bramson shift between the traveling wave solutions and solutions of the Cauchy problem with localized initial data. We find a phase transition depending on how singular f is near u=0 with quite different behavior for more singular f. This is in contrast to the smooth case, that is, when f∈C1,δ, where these behaviors are completely determined by f′(0). In the singular case, several scales appear and require new techniques to understand. © 2021 Elsevier Ltden_US
dc.description.sponsorshipNational Science Foundationen_US
dc.language.isoenen_US
dc.publisherElsevier BVen_US
dc.rights© 2021 Elsevier Ltd. All rights reserved.en_US
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en_US
dc.subjectLogarithmic delayen_US
dc.subjectReaction–diffusion equationsen_US
dc.subjectTraveling wavesen_US
dc.titleThe Bramson delay in a Fisher–KPP equation with log-singular nonlinearityen_US
dc.typeArticleen_US
dc.contributor.departmentDepartment of Mathematics, University of Arizonaen_US
dc.identifier.journalNonlinear Analysis, Theory, Methods and Applicationsen_US
dc.description.note24 month embargo; available online 12 August 2021en_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal accepted manuscripten_US
dc.identifier.piiS0362546X21001644
dc.source.journaltitleNonlinear Analysis
dc.source.volume213
dc.source.beginpage112508


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