Nonlinear stability of traveling wave fronts for delayed reaction diffusion systems

This paper is concerned with nonlinear stability of traveling wave fronts for a delayed reaction diffusion system. We prove that the traveling wave front is exponentially stable to perturbation in some exponentially weighted L∞L∞ spaces, when the difference between initial data and traveling wave front decays exponentially as x→−∞x→−∞, but the initial data can be suitable large in other locations. Moreover, the time decay rates are obtained by weighted energy estimates.