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Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations

Dmitri Finkelshtein Orcid Logo, Yuri Kondratiev, Pasha Tkachov Orcid Logo

Electronic Journal of Differential Equations, Volume: 2019, Issue: 10, Pages: 1 - 27

Swansea University Author: Dmitri Finkelshtein Orcid Logo

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Abstract

We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on R^d. Using the properties of the corresponding semiflow, we prove the existence of monotone traveling waves along...

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Published in: Electronic Journal of Differential Equations
ISSN: 1072-6691
Published: 601 University Drive, San Marcos, TX 78666, USA Department of Mathematics, Texas State University 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa48385
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first_indexed 2019-01-23T05:00:12Z
last_indexed 2019-03-11T14:00:29Z
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spelling 2019-03-11T12:29:22.4648544 v2 48385 2019-01-22 Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2019-01-22 SMA We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on R^d. Using the properties of the corresponding semiflow, we prove the existence of monotone traveling waves along those directions where the diffusion kernel is exponentially integrable. Among other properties, we prove continuity, strict monotonicity and exponential integrability of the traveling wave profiles. Journal Article Electronic Journal of Differential Equations 2019 10 1 27 Department of Mathematics, Texas State University 601 University Drive, San Marcos, TX 78666, USA 1072-6691 Nonlocal diffusion; reaction-diffusion equation; Fisher-KPP equation; traveling waves; nonlocal nonlinearity; anisotropic kernels; integral equation. 22 1 2019 2019-01-22 https://ejde.math.txstate.edu/Volumes/2019/10/abstr.html COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2019-03-11T12:29:22.4648544 2019-01-22T20:36:49.4561463 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Yuri Kondratiev 2 Pasha Tkachov 0000-0002-6773-4506 3 0048385-22012019204219.pdf FKT-trw_exist.pdf 2019-01-22T20:42:19.5870000 Output 598682 application/pdf Accepted Manuscript true 2019-01-22T00:00:00.0000000 This work is licensed under a Creative Commons Attribution 4.0 International License. true eng
title Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations
spellingShingle Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations
Dmitri Finkelshtein
title_short Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations
title_full Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations
title_fullStr Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations
title_full_unstemmed Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations
title_sort Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations
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 Electronic Journal of Differential Equations
container_volume 2019
container_issue 10
container_start_page 1
publishDate 2019
institution Swansea University
issn 1072-6691
publisher Department of Mathematics, Texas State University
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 https://ejde.math.txstate.edu/Volumes/2019/10/abstr.html
document_store_str 1
active_str 0
description We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on R^d. Using the properties of the corresponding semiflow, we prove the existence of monotone traveling waves along those directions where the diffusion kernel is exponentially integrable. Among other properties, we prove continuity, strict monotonicity and exponential integrability of the traveling wave profiles.
published_date 2019-01-22T03:58:49Z
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score 11.012678

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