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Doubly nonlocal Fisher–KPP equation: front propagation

Dmitri Finkelshtein Orcid Logo, Yuri Kondratiev, Pasha Tkachov

Applicable Analysis, Pages: 1 - 24

Swansea University Author: Dmitri Finkelshtein Orcid Logo

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DOI (Published version): 10.1080/00036811.2019.1643011

Abstract

We study propagation over R^d of the solution to a doubly nonlocal reaction-diffusion equation of the Fisher-KPP-type with anisotropic kernels. We present both necessary and sufficient conditions which ensure linear in time propagation of the solution in a direction. For kernels with a finite expone...

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Published in: Applicable Analysis
ISSN: 0003-6811 1563-504X
Published: Informa UK Limited 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa51086
Abstract: We study propagation over R^d of the solution to a doubly nonlocal reaction-diffusion equation of the Fisher-KPP-type with anisotropic kernels. We present both necessary and sufficient conditions which ensure linear in time propagation of the solution in a direction. For kernels with a finite exponential moment over R^d we prove front propagation in all directions for a general class of initial conditions decaying in all directions faster than any exponential function (that includes, for the first time in the literature about the considered type of equations, compactly supported initial conditions).
Keywords: nonlocal diffusion, Fisher-KPP equation, nonlocal nonlinearity, long-time behavior, front propagation, anisotropic kernels, integral equation
College: Faculty of Science and Engineering
Start Page: 1
End Page: 24

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