Journal article 871 views 166 downloads
Doubly nonlocal Fisher–KPP equation: front propagation
Applicable Analysis, Pages: 1 - 24
Swansea University Author: Dmitri Finkelshtein
-
PDF | Accepted Manuscript
Download (509.16KB)
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 |
---|---|
ISSN: | 0003-6811 1563-504X |
Published: |
Informa UK Limited
2019
|
Online Access: |
Check full text
|
URI: | https://cronfa.swan.ac.uk/Record/cronfa51086 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
first_indexed |
2019-07-15T15:34:57Z |
---|---|
last_indexed |
2021-01-12T04:12:48Z |
id |
cronfa51086 |
recordtype |
SURis |
fullrecord |
<?xml version="1.0"?><rfc1807><datestamp>2021-01-11T16:01:50.9010979</datestamp><bib-version>v2</bib-version><id>51086</id><entry>2019-07-15</entry><title>Doubly nonlocal Fisher–KPP equation: front propagation</title><swanseaauthors><author><sid>4dc251ebcd7a89a15b71c846cd0ddaaf</sid><ORCID>0000-0001-7136-9399</ORCID><firstname>Dmitri</firstname><surname>Finkelshtein</surname><name>Dmitri Finkelshtein</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2019-07-15</date><deptcode>SMA</deptcode><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).</abstract><type>Journal Article</type><journal>Applicable Analysis</journal><volume/><journalNumber/><paginationStart>1</paginationStart><paginationEnd>24</paginationEnd><publisher>Informa UK Limited</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0003-6811</issnPrint><issnElectronic>1563-504X</issnElectronic><keywords>nonlocal diffusion, Fisher-KPP equation, nonlocal nonlinearity, long-time behavior, front propagation, anisotropic kernels, integral equation</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2019</publishedYear><publishedDate>2019-12-31</publishedDate><doi>10.1080/00036811.2019.1643011</doi><url>http://dx.doi.org/10.1080/00036811.2019.1643011</url><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2021-01-11T16:01:50.9010979</lastEdited><Created>2019-07-15T09:10:16.5075325</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Dmitri</firstname><surname>Finkelshtein</surname><orcid>0000-0001-7136-9399</orcid><order>1</order></author><author><firstname>Yuri</firstname><surname>Kondratiev</surname><order>2</order></author><author><firstname>Pasha</firstname><surname>Tkachov</surname><order>3</order></author></authors><documents><document><filename>0051086-15072019091316.pdf</filename><originalFilename>FKT-front.pdf</originalFilename><uploaded>2019-07-15T09:13:16.3230000</uploaded><type>Output</type><contentLength>615130</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2020-07-18T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807> |
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 |
_version_ |
1763753245933568000 |
score |
11.028886 |