Nonlinear stability of traveling wave fronts for nonlocal delayed reaction–diffusion equations

This paper is concerned with the nonlinear stability of traveling wave fronts for nonlocal delayed reaction–diffusion equation. We prove that these traveling wave fronts are exponentially stable to perturbation in some exponentially weighted L∞ spaces, when the initial perturbation around the traveling wave fronts decays exponentially as x→−∞, but the initial perturbation can be arbitrary large in other locations. The time decay rate is also obtained by weighted energy estimates.