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The hair-trigger effect for a class of nonlocal nonlinear equations

Dmitri Finkelshtein Orcid Logo, Pasha Tkachov

Nonlinearity, Volume: 31, Issue: 6, Pages: 2442 - 2479

Swansea University Author: Dmitri Finkelshtein Orcid Logo

Abstract

We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on R^d which have only two constant stationary solutions, 0 and \theta>0. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to \infty) to \t...

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Published in: Nonlinearity
ISSN: 0951-7715 1361-6544
Published: IOP Publishing 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa38865
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Abstract: We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on R^d which have only two constant stationary solutions, 0 and \theta>0. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to \infty) to \theta locally uniformly in R^d. We find also sufficient conditions for existence, uniqueness and comparison principle in the considered equations.
Keywords: hair-trigger effect, nonlocal diffusion, reaction-diffusion equation, front propagation, monostable equation, nonlocal nonlinearity, long-time behavior, integral equation
College: College of Science
Issue: 6
Start Page: 2442
End Page: 2479