Existence, uniqueness and stabilityof  traveling wave fronts of discrete quasi-linear equations withdelay

Guangying Lv; Mingxin Wang

doi:10.3934/dcdsb.2010.13.415

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2010, Volume 13, Issue 2: 415-433. Doi: 10.3934/dcdsb.2010.13.415

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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
2.
Science Research Center, Harbin Institute of Technology, Harbin, 150080

Received: November 2008

Revised: April 2009

Published: September 2010

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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.

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