Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 21, Number 5 (2017), 997-1015.
Stability of Traveling Wavefronts for a Delayed Lattice System with Nonlocal Interaction
In this paper, we mainly investigate exponential stability of traveling wavefronts for delayed $2D$ lattice differential equation with nonlocal interaction. For all non-critical traveling wavefronts with the wave speed $c \gt c_*(\theta)$, where $c_*(\theta) \gt 0$ is the critical wave speed and $\theta$ is the direction of propagation, we prove that these traveling waves are asymptotically stable, when the initial perturbation around the traveling waves decay exponentially at far fields, but can be allowed arbitrarily large in other locations. Our approach adopted in this paper is the weighted energy method and the squeezing technique with the help of Gronwall's inequality. Furthermore, from stability result, we prove the uniqueness (up to shift) of the traveling wavefront. Our results can apply to the discrete diffusive Mackey-Glass model and the dicrete diffusive Nicholson's blowflies model on $2D$ lattices.
Taiwanese J. Math., Volume 21, Number 5 (2017), 997-1015.
Received: 12 October 2016
Revised: 15 January 2017
Accepted: 15 January 2017
First available in Project Euclid: 1 August 2017
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Pei, Jingwen; Yu, Zhixian; Zhou, Huiling. Stability of Traveling Wavefronts for a Delayed Lattice System with Nonlocal Interaction. Taiwanese J. Math. 21 (2017), no. 5, 997--1015. doi:10.11650/tjm/7964. https://projecteuclid.org/euclid.twjm/1501599180