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, GE; ZHANG, GUOBAO; and YANG, ZHAO-XING
(2017)
"Stability of nonmonotone critical traveling waves forspatially discrete reaction-diffusion equations with time delay,"
Turkish Journal of Mathematics: Vol. 41:
No.
3, Article 16.
https://doi.org/10.3906/mat-1601-19
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss3/16
