Stability of traveling wave fronts for nonlocal diffusive systems

This paper is concerned with stability of traveling wave fronts for nonlocal diffusive system. We adopt [Formula: see text]-weighted, [Formula: see text]- and [Formula: see text]-energy estimates for the perturbation systems, and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev spaces.