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The hair-trigger effect for a class of nonlocal nonlinear equations

Dmitri Finkelshtein Orcid Logo, Pasha Tkachov

Nonlinearity, Volume: 31, Issue: 6, Pages: 2442 - 2479

Swansea University Author: Dmitri Finkelshtein Orcid Logo

Abstract

We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on R^d which have only two constant stationary solutions, 0 and \theta>0. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to \infty) to \t...

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Published in: Nonlinearity
ISSN: 0951-7715 1361-6544
Published: IOP Publishing 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa38865
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spelling 2020-07-27T15:40:48.3977031 v2 38865 2018-02-23 The hair-trigger effect for a class of nonlocal nonlinear equations 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2018-02-23 SMA We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on R^d which have only two constant stationary solutions, 0 and \theta&#62;0. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to \infty) to \theta locally uniformly in R^d. We find also sufficient conditions for existence, uniqueness and comparison principle in the considered equations. Journal Article Nonlinearity 31 6 2442 2479 IOP Publishing 0951-7715 1361-6544 hair-trigger effect, nonlocal diffusion, reaction-diffusion equation, front propagation, monostable equation, nonlocal nonlinearity, long-time behavior, integral equation 1 6 2018 2018-06-01 10.1088/1361-6544/aab1cb COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2020-07-27T15:40:48.3977031 2018-02-23T14:33:31.4461891 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Pasha Tkachov 2 0038865-23022018143411.pdf FT-HairTrigger-ArXiv-Final.pdf 2018-02-23T14:34:11.6470000 Output 664432 application/pdf Accepted Manuscript true 2019-04-20T00:00:00.0000000 12 month embargo. true eng
title The hair-trigger effect for a class of nonlocal nonlinear equations
spellingShingle The hair-trigger effect for a class of nonlocal nonlinear equations
Dmitri Finkelshtein
title_short The hair-trigger effect for a class of nonlocal nonlinear equations
title_full The hair-trigger effect for a class of nonlocal nonlinear equations
title_fullStr The hair-trigger effect for a class of nonlocal nonlinear equations
title_full_unstemmed The hair-trigger effect for a class of nonlocal nonlinear equations
title_sort The hair-trigger effect for a class of nonlocal nonlinear equations
author_id_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf
author_id_fullname_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein
author Dmitri Finkelshtein
author2 Dmitri Finkelshtein
Pasha Tkachov
format Journal article
container_title Nonlinearity
container_volume 31
container_issue 6
container_start_page 2442
publishDate 2018
institution Swansea University
issn 0951-7715
1361-6544
doi_str_mv 10.1088/1361-6544/aab1cb
publisher IOP Publishing
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
document_store_str 1
active_str 0
description We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on R^d which have only two constant stationary solutions, 0 and \theta&#62;0. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to \infty) to \theta locally uniformly in R^d. We find also sufficient conditions for existence, uniqueness and comparison principle in the considered equations.
published_date 2018-06-01T03:46:55Z
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score 10.927374