Stability of nonmonotone critical traveling waves for spatially discrete reaction-diffusion equations with time delay

Authors : Ge Tian, Guobao Zhang, Zhao-xing Yang

Pages : 655-680

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :This paper is concerned with the existence and stability of critical traveling waves (waves with minimal speed $c=c_*$) for a nonmonotone spatially discrete reaction-diffusion equation with time delay. We first show the existence of critical traveling waves by a limiting argument. Then, using the technical weighted energy method with some new variations, we prove that the critical traveling waves $\phi(x+c_{*}t)$ (monotone or nonmonotone) are time-asymptotically stable when the initial perturbations are small in a certain weighted Sobolev norm.
Keywords : Spatially discrete reaction-diffusion equations, nonmonotone critical traveling waves, stability, weighted energy