Global stability of non-monotone traveling wave solutions for a nonlocal dispersal equation with time delay

This paper is concerned with the global stability of non-monotone traveling wave solutions to a nonlocal dispersion equation with time delay. It is proved that, all noncritical traveling wave solutions are globally stable with the exponential convergence rate t(-1/alpha)e(-mu t) for some constants mu > 0 and alpha is an element of (0,2], and the critical traveling wave solutions are globally stable in the algebraic form t(-1/alpha), where the initial perturbations around the monotone/non-monotone traveling wave solution in a weighted Sobolev space can be arbitrarily large. The adopted approach is the anti-weighted energy method combining with Fourier's transform. (C) 2019 Elsevier Inc. All rights reserved.