### 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:

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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 0003-6811 1563-504X Informa UK Limited 2019 https://cronfa.swan.ac.uk/Record/cronfa36426 No Tags, Be the first to tag this record!
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 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]. nonlocal diffusion; reaction-diffusion equation; front propagation; acceleration; monostable equation; nonlocal nonlinearity; long-time behavior; integral equation College of Science 4 756 780