Taiwanese Journal of Mathematics

Stability of Traveling Wavefronts for a Delayed Lattice System with Nonlocal Interaction

Jingwen Pei, Zhixian Yu, and Huiling Zhou

Full-text: Open access

Abstract

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.

Article information

Source
Taiwanese J. Math., Volume 21, Number 5 (2017), 997-1015.

Dates
Received: 12 October 2016
Revised: 15 January 2017
Accepted: 15 January 2017
First available in Project Euclid: 1 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1501599180

Digital Object Identifier
doi:10.11650/tjm/7964

Mathematical Reviews number (MathSciNet)
MR3707881

Zentralblatt MATH identifier
06871356

Subjects
Primary: 35C07: Traveling wave solutions 92D25: Population dynamics (general) 35B35: Stability

Keywords
traveling wavefronts stability $2D$ lattice weighted energy method squeezing technique

Citation

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


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