Global Stability of Traveling Waves for a More General Nonlocal Reaction-Diffusion Equation

The purpose of this paper is to investigate the global stability of traveling front solutions with noncritical and critical speeds for a more general nonlocal reaction-diffusion equation with or without delay. Our analysis relies on the technical weighted energy method and Fourier transform. Moreover, we can get the rates of convergence and the effect of time-delay on the decay rates of the solutions. Furthermore, according to the stability results, the uniqueness of the traveling front solutions can be proved. Our results generalize and improve the existing results.