Journal article 1210 views 172 downloads
Global stability in a nonlocal reaction-diffusion equation
Stochastics and Dynamics, Volume: 18, Issue: 05, Start page: 1850037
Swansea University Author:
Dmitri Finkelshtein
-
PDF | Accepted Manuscript
Download (487.75KB)
DOI (Published version): 10.1142/S0219493718500375
Abstract
We study stability of stationary solutions for a class of nonlocal semi-linear parabolic equations. To this end, we prove a Feynman-Kac type formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the z...
Published in: | Stochastics and Dynamics |
---|---|
ISSN: | 0219-4937 1793-6799 |
Published: |
World Scientific
2018
|
Online Access: |
Check full text
|
URI: | https://cronfa.swan.ac.uk/Record/cronfa35092 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
first_indexed |
2017-09-04T18:57:30Z |
---|---|
last_indexed |
2019-02-11T11:35:03Z |
id |
cronfa35092 |
recordtype |
SURis |
fullrecord |
<?xml version="1.0"?><rfc1807><datestamp>2019-02-07T20:21:51.9302387</datestamp><bib-version>v2</bib-version><id>35092</id><entry>2017-09-04</entry><title>Global stability in a nonlocal reaction-diffusion equation</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>2017-09-04</date><deptcode>SMA</deptcode><abstract>We study stability of stationary solutions for a class of nonlocal semi-linear parabolic equations. To this end, we prove a Feynman-Kac type formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the zero solution, and use them to the study of the spatial logistic equation arising in population ecology. For this equation, we find conditions which imply that its positive stationary solution is asymptotically stable. We consider also the case when the initial condition is given by a random field.</abstract><type>Journal Article</type><journal>Stochastics and Dynamics</journal><volume>18</volume><journalNumber>05</journalNumber><paginationStart>1850037</paginationStart><publisher/><placeOfPublication>World Scientific</placeOfPublication><issnPrint>0219-4937</issnPrint><issnElectronic>1793-6799</issnElectronic><keywords>Nonlocal diffusion; Feynman--Kac formula; L\&apos;{e}vy processes; Reaction-diffusion equation; Semilinear parabolic equation; Monostable equation; Nonlocal nonlinearity</keywords><publishedDay>28</publishedDay><publishedMonth>9</publishedMonth><publishedYear>2018</publishedYear><publishedDate>2018-09-28</publishedDate><doi>10.1142/S0219493718500375</doi><url>http://www.worldscientific.com/worldscinet/sd</url><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2019-02-07T20:21:51.9302387</lastEdited><Created>2017-09-04T15:13:35.8891618</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>Stanislav</firstname><surname>Molchanov</surname><order>3</order></author><author><firstname>Pasha</firstname><surname>Tkachov</surname><order>4</order></author></authors><documents><document><filename>0035092-04092017152239.pdf</filename><originalFilename>FKMT-ArXiv-v2.pdf</originalFilename><uploaded>2017-09-04T15:22:39.8970000</uploaded><type>Output</type><contentLength>446968</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2017-09-05T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807> |
spelling |
2019-02-07T20:21:51.9302387 v2 35092 2017-09-04 Global stability in a nonlocal reaction-diffusion equation 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2017-09-04 SMA We study stability of stationary solutions for a class of nonlocal semi-linear parabolic equations. To this end, we prove a Feynman-Kac type formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the zero solution, and use them to the study of the spatial logistic equation arising in population ecology. For this equation, we find conditions which imply that its positive stationary solution is asymptotically stable. We consider also the case when the initial condition is given by a random field. Journal Article Stochastics and Dynamics 18 05 1850037 World Scientific 0219-4937 1793-6799 Nonlocal diffusion; Feynman--Kac formula; L\'{e}vy processes; Reaction-diffusion equation; Semilinear parabolic equation; Monostable equation; Nonlocal nonlinearity 28 9 2018 2018-09-28 10.1142/S0219493718500375 http://www.worldscientific.com/worldscinet/sd COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2019-02-07T20:21:51.9302387 2017-09-04T15:13:35.8891618 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Yuri Kondratiev 2 Stanislav Molchanov 3 Pasha Tkachov 4 0035092-04092017152239.pdf FKMT-ArXiv-v2.pdf 2017-09-04T15:22:39.8970000 Output 446968 application/pdf Accepted Manuscript true 2017-09-05T00:00:00.0000000 true eng |
title |
Global stability in a nonlocal reaction-diffusion equation |
spellingShingle |
Global stability in a nonlocal reaction-diffusion equation Dmitri Finkelshtein |
title_short |
Global stability in a nonlocal reaction-diffusion equation |
title_full |
Global stability in a nonlocal reaction-diffusion equation |
title_fullStr |
Global stability in a nonlocal reaction-diffusion equation |
title_full_unstemmed |
Global stability in a nonlocal reaction-diffusion equation |
title_sort |
Global stability in a nonlocal reaction-diffusion equation |
author_id_str_mv |
4dc251ebcd7a89a15b71c846cd0ddaaf |
author_id_fullname_str_mv |
4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein |
author |
Dmitri Finkelshtein |
author2 |
Dmitri Finkelshtein Yuri Kondratiev Stanislav Molchanov Pasha Tkachov |
format |
Journal article |
container_title |
Stochastics and Dynamics |
container_volume |
18 |
container_issue |
05 |
container_start_page |
1850037 |
publishDate |
2018 |
institution |
Swansea University |
issn |
0219-4937 1793-6799 |
doi_str_mv |
10.1142/S0219493718500375 |
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://www.worldscientific.com/worldscinet/sd |
document_store_str |
1 |
active_str |
0 |
description |
We study stability of stationary solutions for a class of nonlocal semi-linear parabolic equations. To this end, we prove a Feynman-Kac type formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the zero solution, and use them to the study of the spatial logistic equation arising in population ecology. For this equation, we find conditions which imply that its positive stationary solution is asymptotically stable. We consider also the case when the initial condition is given by a random field. |
published_date |
2018-09-28T03:43:33Z |
_version_ |
1763752032141836288 |
score |
11.021648 |