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. For more information see https://ejde.math.txstate.edu/Volumes/2020/46/abstr.html