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

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.

Keywords

• delay reaction-diffusion system
• traveling waves
• global stability
• fourier transform
• weighted energy method