# American Institute of Mathematical Sciences

doi: 10.3934/era.2021003

## Global stability of traveling waves for a spatially discrete diffusion system with time delay

 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China

* Corresponding author: Guo-Bao Zhang

Received  September 2020 Revised  November 2020 Published  January 2021

Fund Project: The second author is supported by NSF of China (11861056)

This article deals with the global stability of traveling waves of a spatially discrete diffusion system with time delay and without quasi-monotonicity. Using the Fourier transform and the weighted energy method with a suitably selected weighted function, we prove that the monotone or non-monotone traveling waves are exponentially stable in $L^\infty(\mathbb{R})\times L^\infty(\mathbb{R})$ with the exponential convergence rate $e^{-\mu t}$ for some constant $\mu>0$.

Citation: Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, doi: 10.3934/era.2021003
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