### Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line

Dmitri Finkelshtein , Pasha Tkachov

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

Swansea University Author:

• PDF | Accepted Manuscript

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 0003-6811 1563-504X Informa UK Limited 2019 https://cronfa.swan.ac.uk/Record/cronfa36426 No Tags, Be the first to tag this record!
first_indexed 2017-11-01T19:54:01Z 2020-07-14T13:02:19Z cronfa36426 SURis 2020-07-14T11:59:37.7461365v2364262017-11-01Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line4dc251ebcd7a89a15b71c846cd0ddaaf0000-0001-7136-9399DmitriFinkelshteinDmitri Finkelshteintruefalse2017-11-01SMAWe 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 ArticleApplicable Analysis984756780Informa UK Limited0003-68111563-504Xnonlocal diffusion; reaction-diffusion equation; front propagation; acceleration; monostable equation; nonlocal nonlinearity; long-time behavior; integral equation12320192019-03-1210.1080/00036811.2017.1400537COLLEGE NANMEMathematicsCOLLEGE CODESMASwansea University2020-07-14T11:59:37.74613652017-11-01T13:39:54.6727070Faculty of Science and EngineeringSchool of Mathematics and Computer Science - MathematicsDmitriFinkelshtein0000-0001-7136-93991PashaTkachov20036426-01112017134123.pdfFT-Acceleration-1D-final.pdf2017-11-01T13:41:23.6270000Output537420application/pdfAccepted Manuscripttrue2018-11-13T00:00:00.0000000trueeng 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 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 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 COLLEGE CODE SMA 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 Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line Dmitri Finkelshtein Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line 4dc251ebcd7a89a15b71c846cd0ddaaf 4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein Dmitri Finkelshtein Dmitri Finkelshtein Pasha Tkachov Journal article Applicable Analysis 98 4 756 2019 Swansea University 0003-6811 1563-504X 10.1080/00036811.2017.1400537 Informa UK Limited Faculty of Science and Engineering facultyofscienceandengineering Faculty of Science and Engineering facultyofscienceandengineering Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics 1 0 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]. 2019-03-12T03:41:08Z 1756870285632471040 10.9274