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Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line

Dmitri Finkelshtein Orcid Logo, Pasha Tkachov

Applicable Analysis, Volume: 98, Issue: 4, Pages: 756 - 780

Swansea University Author: Dmitri Finkelshtein Orcid Logo

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DOI (Published version): 10.1080/00036811.2017.1400537

Abstract

We consider the accelerated propagation of solutions to equations with a nonlocal linear dispersion on the real line and monostable nonlinearities (both local or nonlocal, however, not degenerated at $0$), in the case when either of the dispersion kernel or the initial condition has regularly heavy...

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Published in: Applicable Analysis
ISSN: 0003-6811 1563-504X
Published: Informa UK Limited 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa36426
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spelling 2020-07-14T11:59:37.7461365 v2 36426 2017-11-01 Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2017-11-01 MACS We consider the accelerated propagation of solutions to equations with a nonlocal linear dispersion on the real line and monostable nonlinearities (both local or nonlocal, however, not degenerated at $0$), in the case when either of the dispersion kernel or the initial condition has regularly heavy tails at both $\pm\infty$, perhaps different. We show that, in such case, the propagation in the right direction is fully determined by the right tails of either the kernel or the initial condition. We describe both cases of integrable and monotone initial conditions which may give different orders of the acceleration. Our approach is based, in particular, on the extension of the theory of sub-exponential distributions, which we introduced early in [D. Finkelshtein, P. Tkachov. 'Kesten's bound for sub-exponential densities on the real line and its multi-dimensional analogues', Advances in Applied Probability, 2018, 50(2), 373-395]. Journal Article Applicable Analysis 98 4 756 780 Informa UK Limited 0003-6811 1563-504X nonlocal diffusion; reaction-diffusion equation; front propagation; acceleration; monostable equation; nonlocal nonlinearity; long-time behavior; integral equation 12 3 2019 2019-03-12 10.1080/00036811.2017.1400537 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2020-07-14T11:59:37.7461365 2017-11-01T13:39:54.6727070 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Pasha Tkachov 2 0036426-01112017134123.pdf FT-Acceleration-1D-final.pdf 2017-11-01T13:41:23.6270000 Output 537420 application/pdf Accepted Manuscript true 2018-11-13T00:00:00.0000000 true eng
title Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line
spellingShingle Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line
Dmitri Finkelshtein
title_short Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line
title_full Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line
title_fullStr Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line
title_full_unstemmed Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line
title_sort Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line
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 Applicable Analysis
container_volume 98
container_issue 4
container_start_page 756
publishDate 2019
institution Swansea University
issn 0003-6811
1563-504X
doi_str_mv 10.1080/00036811.2017.1400537
publisher Informa UK Limited
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
document_store_str 1
active_str 0
description We consider the accelerated propagation of solutions to equations with a nonlocal linear dispersion on the real line and monostable nonlinearities (both local or nonlocal, however, not degenerated at $0$), in the case when either of the dispersion kernel or the initial condition has regularly heavy tails at both $\pm\infty$, perhaps different. We show that, in such case, the propagation in the right direction is fully determined by the right tails of either the kernel or the initial condition. We describe both cases of integrable and monotone initial conditions which may give different orders of the acceleration. Our approach is based, in particular, on the extension of the theory of sub-exponential distributions, which we introduced early in [D. Finkelshtein, P. Tkachov. 'Kesten's bound for sub-exponential densities on the real line and its multi-dimensional analogues', Advances in Applied Probability, 2018, 50(2), 373-395].
published_date 2019-03-12T19:21:18Z
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score 11.047674

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