Electron. J. Diff. Equ., Vol. 2013 (2013), No. 119, pp. 1-15.

Asymptotic stability of traveling fronts in delayed reaction-diffusion monostable equations on higher-dimensional lattices

Hai-Qin Zhao

This article is concerned with traveling wave fronts for spatially discrete delayed reaction-diffusion equations on higher-dimensional lattices. Under the monostable assumption and some reasonable conditions, we prove the globally asymptotic stability of traveling wave fronts in the sense of phase shift by using the comparison principle and the squeezing technique.

Submitted December 14, 2012. Published May 10, 2013.
Math Subject Classifications: 35K57, 35B40, 92D25.
Key Words: Traveling wave front; lattice differential equation; delay; monostable nonlinearity

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Hai-Qin Zhao
College of Mathematics and Information Science
Xianyang Normal University
Xianyang, Shaanxi 712000, China
email: xinyi98_01@126.com

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