Shi-Liang Wu, Tian-Tian Liu
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
, where
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 4, 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.
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Shi-Liang Wu Department of Mathematics, Xidian University Xi'an, Shaanxi 710071, China email: slwu@xidian.edu.cn | |
Tian-Tian Liu Department of Mathematics, Xidian University Xi'an, Shaanxi 710071, China email: ahtian4402@qq.com |
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