Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 179, pp. 1-14.

Title: Exponential stability of traveling  fronts for a 2D lattice 
       delayed differential equation  with global interaction

Authors: Shi-Liang Wu (Xidian Univ., Xi'an, Shaanxi, China)
         Tian-Tian Liu (Xidian Univ., Xi'an, Shaanxi, China)

Abstract:
 The purpose of this paper is to study traveling wave fronts of  a
 two-dimensional (2D) lattice  delayed differential equation  with global
 interaction. Applying the comparison principle combined with the
 technical weighted-energy method, we prove that  any given traveling wave
 front with large speed is time-asymptotically stable when the initial
 perturbation around the wave front need  decay to zero exponentially as
  $i \cos\theta +j \sin\theta\to -\infty$, where $\theta$ is
 the direction of propagation, but it can be allowed relatively large in
 other locations. The result essentially extends the stability of traveling
  wave fronts for local delayed lattice differential equations obtained
  by Cheng et al [1] and Yu and Ruan [16].

Submitted July 1, 2013. Published August 04, 2013.
Math Subject Classifications: 35K57, 35R10, 35B40, 92D25.
Key Words: Exponential stability; traveling wave front; global interaction;
           lattice differential equation;  comparison principle;
           weighted energy method.