On travelling wavefronts of Nicholson's blowflies equation with diffusion

Abstract

This paper is devoted to the study of Nicholson's blowflies equation with diffusion: a kind of time-delayed reaction diffusion. For any travelling wavefront with speed c > c * ( c * is the minimum wave speed), we prove that the wavefront is time-asymptotically stable when the delay-time is sufficiently small, and the initial perturbation around the wavefront decays to zero exponentially in space as x → −∞, but it can be large in other locations. The result develops and improves the previous wave stability obtained by Mei et al . in 2004. The new approach developed in this paper is the comparison principle combined with the technical weighted-energy method. Numerical simulations are also carried out to confirm our theoretical results.