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^\infty(\mathbb{R})\times L^\infty(\mathbb{R}) $ with the exponential convergence rate $ e^{-\mu t} $ for some constant $ \mu>0 $.
Citation: Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay[J]. Electronic Research Archive, 2021, 29(4): 2599-2618. doi: 10.3934/era.2021003
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^\infty(\mathbb{R})\times L^\infty(\mathbb{R}) $ with the exponential convergence rate $ e^{-\mu t} $ for some constant $ \mu>0 $.
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