@article{068a3d86a29444848cd5d660da4055b3,
title = "Thin front limit of an integro-differential fisher-kpp equation with fat-tailed kernels",
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.",
keywords = "Asymptotic analysis, Asymptotic limit, Exponential speed of propagation, Fat-tailed kernels, Fisher-KPP equation, Front acceleration, Hamilton--Jacobi equation, Integro-differential equations",
author = "Emeric Bouin and Jimmy Garnier and Christopher Henderson and Florian Patout",
note = "Funding Information: Part of this work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of Universit\'e de Lyon, within the program ``Investissements d'Avenir{"}{"} (ANR-11- IDEX-0007) and the project NONLOCAL (ANR-14-CE25-0013) operated by the French National Research Agency (ANR). In addition, this project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement 639638). The third author's work was partially supported by the National Science Foundation Research Training Group grant DMS-1246999. Funding Information: \ast Received by the editors May 31, 2017; accepted for publication (in revised form) March 13, 2018; published electronically June 26, 2018. http://www.siam.org/journals/sima/50-3/M113250.html Funding: Part of this work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of Universit\e' de Lyon, within the program ``Investissements d'Avenir{"}{"} (ANR-11-IDEX-0007) and the project NONLOCAL (ANR-14-CE25-0013) operated by the French National Research Agency (ANR). In addition, this project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement 639638). The third author's work was partially supported by the National Science Foundation Research Training Group grant DMS-1246999. Publisher Copyright: \bigcirc c 2018 Society for Industrial and Applied Mathematics",
year = "2018",
doi = "10.1137/17M1132501",
language = "English (US)",
volume = "50",
pages = "3365--3394",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}