GLOBAL STABILITY OF TRAVELING WAVES FOR A SPATIALLY DISCRETE DIFFUSION SYSTEM WITH TIME DELAY

This article deals with the global stability of traveling waves of a spatially discrete diffusion system with time delay and without quasi-monotonicity. Using the Fourier transform and the weighted energy method with a suitably selected weighted function, we prove that the monotone or non-monotone traveling waves are exponentially stable in L-infinity(R) x L-infinity(R) with the exponential convergence rate e(-mu t) for some constant mu > 0.