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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
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first_indexed 2019-07-15T15:34:57Z
last_indexed 2021-01-12T04:12:48Z
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spelling 2021-01-11T16:01:50.9010979 v2 51086 2019-07-15 Doubly nonlocal Fisher–KPP equation: front propagation 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2019-07-15 SMA 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). Journal Article Applicable Analysis 1 24 Informa UK Limited 0003-6811 1563-504X nonlocal diffusion, Fisher-KPP equation, nonlocal nonlinearity, long-time behavior, front propagation, anisotropic kernels, integral equation 31 12 2019 2019-12-31 10.1080/00036811.2019.1643011 http://dx.doi.org/10.1080/00036811.2019.1643011 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2021-01-11T16:01:50.9010979 2019-07-15T09:10:16.5075325 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Yuri Kondratiev 2 Pasha Tkachov 3 0051086-15072019091316.pdf FKT-front.pdf 2019-07-15T09:13:16.3230000 Output 615130 application/pdf Accepted Manuscript true 2020-07-18T00:00:00.0000000 true eng
title Doubly nonlocal Fisher–KPP equation: front propagation
spellingShingle Doubly nonlocal Fisher–KPP equation: front propagation
Dmitri Finkelshtein
title_short Doubly nonlocal Fisher–KPP equation: front propagation
title_full Doubly nonlocal Fisher–KPP equation: front propagation
title_fullStr Doubly nonlocal Fisher–KPP equation: front propagation
title_full_unstemmed Doubly nonlocal Fisher–KPP equation: front propagation
title_sort Doubly nonlocal Fisher–KPP equation: front propagation
author_id_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf
author_id_fullname_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein
author Dmitri Finkelshtein
author2 Dmitri Finkelshtein
Yuri Kondratiev
Pasha Tkachov
format Journal article
container_title Applicable Analysis
container_start_page 1
publishDate 2019
institution Swansea University
issn 0003-6811
1563-504X
doi_str_mv 10.1080/00036811.2019.1643011
publisher Informa UK Limited
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://dx.doi.org/10.1080/00036811.2019.1643011
document_store_str 1
active_str 0
description 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).
published_date 2019-12-31T04:02:51Z
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score 11.014067

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