Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion

Abstract

This paper considers the nonlinear stability oftravelling wavefronts of a time-delayed diffusive Nicholson blowflies equation. We prove that, under a weighted L 2 norm, ifa solution is sufficiently close to a travelling wave front initially, it converges exponentially to the wavefront as t → ∞. The rate ofconvergence is also estimated.