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

Finkelshtein, Dmitri; Kondratiev, Yuri; Tkachov, Pasha

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

Dmitri Finkelshtein

, Yuri Kondratiev, Pasha Tkachov

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

Swansea University Author: Dmitri Finkelshtein

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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
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa48385

first_indexed	2019-01-23T05:00:12Z
last_indexed	2019-03-11T14:00:29Z
id	cronfa48385
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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 MACS 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 and Computer Science School COLLEGE CODE MACS 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
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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
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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	2019-01-22T19:44:22Z
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score	11.047674

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

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