Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1601-19
Keywords
Spatially discrete reaction-diffusion equations, nonmonotone critical traveling waves, stability, weighted energy
First Page
655
Last Page
680
Recommended Citation
TIAN, G, ZHANG, G, & YANG, Z (2017). Stability of nonmonotone critical traveling waves forspatially discrete reaction-diffusion equations with time delay. Turkish Journal of Mathematics 41 (3): 655-680. https://doi.org/10.3906/mat-1601-19
