Abstract
In this paper, we study the existence and stability of traveling waves of infinite-dimensional lattice differential equations with time delay, where the equation may be not quasi-monotone. Firstly, by applying Schauder’s fixed point theorem, we get the existence of traveling waves with the speed c > c∗ (here c∗ is the minimal wave speed). Using a limiting argument, the existence of traveling waves with wave speed c = c∗ is also established. Secondly, for sufficiently small initial perturbations, the asymptotic stability of the traveling waves \(\boldsymbol {\Phi }:=\{{\Phi }(n+ct)\}_{n\in \mathbb {Z}}\) with the wave speed c > c∗ is proved. Here we emphasize that the traveling waves \(\boldsymbol {\Phi }:=\{{\Phi }(n+ct)\}_{n\in \mathbb {Z}}\) may be non-monotone.
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The authors are grateful to the anonymous referee for her/his very valuable comments and suggestions helping to the improvement of the manuscript.
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This work was supported by NNSF of China (11371179).
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Tian, G., Liu, L. & Wang, ZC. Existence and Stability of Traveling Waves for Infinite-Dimensional Delayed Lattice Differential Equations. J Dyn Control Syst 26, 311–331 (2020). https://doi.org/10.1007/s10883-019-09452-7
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DOI: https://doi.org/10.1007/s10883-019-09452-7