Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 46, pp. 1-18.

Title: Global stability of traveling waves for delay reaction-diffusion systems 
       without quasi-monotonicity
       
Authors: Si Su  (Northwest Normal Univ., Lanzhou, Gansu, China)
         Guo-Bao Zhang (Northwest Normal Univ., Lanzhou, Gansu, China)

Abstract:
 This article concerns the global stability of traveling waves of a reaction-diffusion
 system with delay and without quasi-monotonicity. We prove that the traveling
 waves (monotone or non-monotone) are exponentially stable in $L^\infty(\mathbb{R})$
 with the exponential convergence rate $t^{-1/2}e^{-\mu t}$ for some constant $\mu>0$.
 We use the Fourier transform and the weighted energy method with a suitably weight 
 function.
 
Submitted December 8, 2019. Published May 19, 2020.
Math Subject Classifications: 35C07, 35B35, 92D30.
Key Words: Delay reaction-diffusion system; traveling waves; global stability;
           Fourier transform; weighted energy method.