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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 415 - 433, Volume 13, Issue 2, March 2010      doi:10.3934/dcdsb.2010.13.415

 
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Guangying Lv - Department of Mathematics, Southeast University, Nanjing 210018, China (email)
Mingxin Wang - Science Research Center, Harbin Institute of Technology, Harbin, 150080, China (email)

Abstract: 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, 58D25.

Received: November 2008;      Revised: April 2009;      Available Online: December 2009.