Thin front limit of an integro-differential fisher-kpp equation with fat-tailed kernels

Emeric Bouin, Jimmy Garnier, Christopher Henderson, Florian Patout

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

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. First, 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 (superlinear) spreading rate in the Hamilton--Jacobi sense by means of sub- and supersolutions. Second, 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.

Original languageEnglish (US)
Pages (from-to)3365-3394
Number of pages30
JournalSIAM Journal on Mathematical Analysis
Volume50
Issue number3
DOIs
StatePublished - 2018
Externally publishedYes

Keywords

  • Asymptotic analysis
  • Asymptotic limit
  • Exponential speed of propagation
  • Fat-tailed kernels
  • Fisher-KPP equation
  • Front acceleration
  • Hamilton--Jacobi equation
  • Integro-differential equations

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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