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
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01528812
Journal nameSIAM Journal on Mathematical Analysis
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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 / Keywordsintegro-differential Fisher-KPP equation
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