Traveling wavefronts in temporally discrete reaction-diffusion equations with delay

This paper is concerned with the existence of traveling wavefronts of a temporally discrete reaction-diffusion equation with delay. By using monotone iteration and upper-lower solution technique, the existence of traveling wavefronts for the temporally discrete reaction-diffusion equation with delay is established. As an application, we consider an abstract diffusive equation, which includes a single species diffusive model as a particular case. Our result implies the temporally discrete model is a good approximation of corresponding continuous time model in sense of propagation. (c) 2006 Elsevier Ltd. All rights reserved.