American Institute of Mathematical Sciences

Advanced
March  2010, 13(2): 415-433. doi: 10.3934/dcdsb.2010.13.415

Existence, uniqueness and stability of traveling wave fronts of discrete quasi-linear equations with delay

Guangying Lv 1, and  Mingxin Wang 2,

1. 

Department of Mathematics, Southeast University, Nanjing 210018, China
2. 

Science Research Center, Harbin Institute of Technology, Harbin, 150080, China

Received  November 2008 Revised  April 2009 Published  December 2009

This paper is concerned with the existence, uniqueness and asymptotically stability of traveling wave fronts of discrete quasi-linear equations with delay. We first establish the existence of traveling wave fronts by using the super-sub solution and monotone iteration technique. Then we show that the traveling wave front is unique up to a translation. At last, we employ the comparison principle and the squeezing technique to prove that the traveling wave front is globally asymptotic stable with phase shift.
Keywords: Existence; Uniqueness; Stability; Traveling wave fronts; Discrete quasi-linear equations; Delay..
Mathematics Subject Classification: Primary: 34K30; 35B40; Secondary: 35R10, 58D2.
Citation: Guangying Lv, Mingxin Wang. Existence, uniqueness and stability of traveling wave fronts of discrete quasi-linear equations with delay. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 415-433. doi: 10.3934/dcdsb.2010.13.415
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