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Thin front limit of an integro–differential Fisher–KPP equation with fat–tailed kernels

Bouin, Emeric; Garnier, Jimmy; Henderson, Christopher; Patout, Florian (2018), Thin front limit of an integro–differential Fisher–KPP equation with fat–tailed kernels, SIAM Journal on Mathematical Analysis, 50, 3, p. 3365-3394. 10.1137/17M1132501

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01528812
Date
2018
Journal name
SIAM Journal on Mathematical Analysis
Volume
50
Number
3
Publisher
SIAM
Pages
3365-3394
Publication identifier
Metadata
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Author(s)
Bouin, Emeric

Garnier, Jimmy cc

Henderson, Christopher

Patout, Florian
Abstract (EN)
We study the asymptotic behavior of solutions to a monostable integro-differential Fisher-KPP equation , that is where the standard Laplacian is replaced by a convolution term, when the dispersal kernel is fat-tailed. We focus on two different regimes. Firstly, we study the long time/long range scaling limit by introducing a relevant rescaling in space and time and prove a sharp bound on the (super-linear) spreading rate in the Hamilton-Jacobi sense by means of sub-and super-solutions. Secondly, we investigate a long time/small mutation regime for which, after identifying a relevant rescaling for the size of mutations, we derive a Hamilton-Jacobi limit.
Subjects / Keywords
integro-differential Fisher-KPP equation