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∞ (ℝ) with the exponential convergence rate t-1/2 e-μt for some constant μ > 0. We use the Fourier transform and the weighted energy method with a suitably weight function.