Journal article 768 views 146 downloads
Doubly nonlocal Fisher–KPP equation: front propagation
Dmitri Finkelshtein 
,
Yuri Kondratiev,
Pasha Tkachov
,
Yuri Kondratiev,
Pasha Tkachov
Applicable Analysis, Pages: 1 - 24
Swansea University Author:
Dmitri Finkelshtein
-
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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...
| Published in: | Applicable Analysis |
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| ISSN: | 0003-6811 1563-504X |
| Published: |
Informa UK Limited
2019
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa51086 |
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| 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). |
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| 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 |