Traveling Wave for Reaction Diffusion Equation with Spatio-Temporal Delay

Abstract

In this paper, we study the traveling wave fronts of reaction diffusion system with spatio-temporal delay. With some particular delay kernel, the nonlocal equation is reduced to a system of singularly perturbed ODEs. It is proved, by use of geometric singular perturbation analysis and Fredholm theory, that the traveling wave front persists when the delay is suitably small and it is qualitatively similar to those of the undelayed reaction diffusion system.