Stability of traveling wavefronts in discrete reaction-diffusion   equations with nonlocal delay effects
  This paper deals with traveling wavefronts for temporally delayed, spatially discrete reaction-diffusion equations. Using a combination of the weighted energy method and the Green function technique, we prove that all noncritical wavefronts are globally exponentially stable, and critical wavefronts are globally algebraically stable when the initial perturbations around the wavefront decay to zero exponentially near minus infinity regardless of the magnitude of time delay. 
Shangjiang Guo and Johannes Zimmer
math.DS