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Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case

Dmitri Finkelshtein Orcid Logo, Yuri Kondratiev, Pasha Tkachov

Journal of Elliptic and Parabolic Equations, Volume: 5, Issue: 2, Pages: 423 - 471

Swansea University Author: Dmitri Finkelshtein Orcid Logo

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DOI (Published version): 10.1007/s41808-019-00045-w

Abstract

We describe acceleration of the front propagation for solutions to a class of monostable nonlinear equations with a nonlocal diffusion in $\mathbb{R}^d$, $d\geq1$. We show that the acceleration takes place if either the diffusion kernel or the initial condition has `regular' heavy tails in $\X$...

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Published in: Journal of Elliptic and Parabolic Equations
ISSN: 2296-9020 2296-9039
Published: Springer Science and Business Media LLC 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa52633
first_indexed 2019-11-02T19:12:40Z
last_indexed 2020-11-21T04:06:59Z
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spelling 2020-11-20T10:27:36.2445658 v2 52633 2019-11-02 Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2019-11-02 MACS We describe acceleration of the front propagation for solutions to a class of monostable nonlinear equations with a nonlocal diffusion in $\mathbb{R}^d$, $d\geq1$. We show that the acceleration takes place if either the diffusion kernel or the initial condition has `regular' heavy tails in $\X$ (in particular, decays slower than exponentially). Under general assumptions which can be verified for particular models, we present sharp estimates for the time-space zone which separates the region of convergence to the unstable zero solution with the region of convergence to the stable positive constant solution. We show the variety of different possible rates of the propagation starting from a little bit faster than a linear one up to the exponential rate. The paper generalizes to the case $d>1$ our results for the case $d=1$ obtained early in Finkelshtein and Tkachov (Appl Anal 98(4):756–780, 2019). Journal Article Journal of Elliptic and Parabolic Equations 5 2 423 471 Springer Science and Business Media LLC 2296-9020 2296-9039 1 12 2019 2019-12-01 10.1007/s41808-019-00045-w COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2020-11-20T10:27:36.2445658 2019-11-02T17:37:51.8122512 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 52633__15779__3d1544354e3f462b8a52a00ed83520b2.pdf FKT-Acceleration-Multidim-Mod2.pdf 2019-11-02T17:42:57.3594839 Output 755787 application/pdf Accepted Manuscript true 2020-11-01T00:00:00.0000000 true eng
title Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case
spellingShingle Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case
Dmitri Finkelshtein
title_short Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case
title_full Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case
title_fullStr Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case
title_full_unstemmed Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case
title_sort Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case
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 Journal of Elliptic and Parabolic Equations
container_volume 5
container_issue 2
container_start_page 423
publishDate 2019
institution Swansea University
issn 2296-9020
2296-9039
doi_str_mv 10.1007/s41808-019-00045-w
publisher Springer Science and Business Media LLC
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 describe acceleration of the front propagation for solutions to a class of monostable nonlinear equations with a nonlocal diffusion in $\mathbb{R}^d$, $d\geq1$. We show that the acceleration takes place if either the diffusion kernel or the initial condition has `regular' heavy tails in $\X$ (in particular, decays slower than exponentially). Under general assumptions which can be verified for particular models, we present sharp estimates for the time-space zone which separates the region of convergence to the unstable zero solution with the region of convergence to the stable positive constant solution. We show the variety of different possible rates of the propagation starting from a little bit faster than a linear one up to the exponential rate. The paper generalizes to the case $d>1$ our results for the case $d=1$ obtained early in Finkelshtein and Tkachov (Appl Anal 98(4):756–780, 2019).
published_date 2019-12-01T07:37:46Z
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score 11.0578165

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