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Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line / Dmitri, Finkelshtein

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

Swansea University Author: Dmitri, Finkelshtein

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: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa36426
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spelling 2019-10-17T17:41:48.9841989 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 SMA 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 0003-6811 1563-504X nonlocal diffusion; reaction-diffusion equation; front propagation; acceleration; monostable equation; nonlocal nonlinearity; long-time behavior; integral equation 1 1 2019 2019-01-01 10.1080/00036811.2017.1400537 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2019-10-17T17:41:48.9841989 2017-11-01T13:39:54.6727070 College of 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 12 month embargo. 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
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doi_str_mv 10.1080/00036811.2017.1400537
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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 2019-01-01T19:01:08Z
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