LAUSR

Abstract 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 / α e − μ t for some constants μ > 0 and α ∈ ( 0 , 2 ] , and the critical traveling wave solutions are globally stable in the algebraic form t − 1 / α , 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.