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The Bramson logarithmic delay in the cane toads equations

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Date
2017
Link to item file
https://hal.archives-ouvertes.fr/hal-01379324
Dewey
Analyse
Sujet
PDE
Journal issue
Quarterly of Applied Mathematics
Volume
75
Number
4
Publication date
2017
Article pages
599-634
Publisher
AMS
DOI
http://dx.doi.org/10.1090/qam/1470
URI
https://basepub.dauphine.fr/handle/123456789/17236
Collections
  • CEREMADE : Publications
Metadata
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Author
Bouin, Emeric
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Henderson, Christopher
106 Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Ryzhik, Lenya
173436 Department of Mathematics, Stanford University
Type
Article accepté pour publication ou publié
Abstract (EN)
We study a nonlocal reaction-diffusion-mutation equation modeling the spreading of a cane toads population structured by a phenotypical trait responsible for the spatial diffusion rate. When the trait space is bounded, the cane toads equation admits traveling wave solutions [7]. Here, we prove a Bramson type spreading result: the lag between the position of solutions with localized initial data and that of the traveling waves grows as (3/(2λ *)) log t. This result relies on a present-time Harnack inequality which allows to compare solutions of the cane toads equation to those of a Fisher-KPP type equation that is local in the trait variable.

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