Electron. J. Differential Equations, Vol. 2020 (2020), No. 46, pp. 1-18.

Global stability of traveling waves for delay reaction-diffusion systems without quasi-monotonicity

Si Su, Guo-Bao Zhang

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.
DOI: 10.58997/ejde.2020.46

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Si Su
College of Mathematics and Statistics
Northwest Normal University
Lanzhou, Gansu 730070, China
email: 18809422634@163.com
Guo-Bao Zhang
College of Mathematics and Statistics
Northwest Normal University
Lanzhou, Gansu 730070, China
email: zhanggb2011@nwnu.edu.cn

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