Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2018

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

Résumé

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.

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Dates et versions

hal-01528812 , version 1 (30-05-2017)
hal-01528812 , version 2 (18-04-2018)

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Emeric Bouin, Jimmy Garnier, Christopher Henderson, Florian Patout. Thin front limit of an integro–differential Fisher–KPP equation with fat–tailed kernels. SIAM Journal on Mathematical Analysis, 2018, 50 (3), pp.3365-3394. ⟨10.1137/17M1132501⟩. ⟨hal-01528812v2⟩
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