The Bramson logarithmic delay in the cane toads equations

Bouin, Emeric; Henderson, Christopher; Ryzhik, Lenya

Bouin, Emeric; Henderson, Christopher; Ryzhik, Lenya (2017), The Bramson logarithmic delay in the cane toads equations, Quarterly of Applied Mathematics, 75, 4, p. 599-634. 10.1090/qam/1470

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01379324

Date

2017

Journal name

Quarterly of Applied Mathematics

Volume

Number

Publisher

AMS

Pages

599-634

Publication identifier

10.1090/qam/1470

Metadata

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Author(s)

Bouin, Emeric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Henderson, Christopher
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Ryzhik, Lenya

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.

Subjects / Keywords

PDE