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July  2009, 12(1): 219-225. doi: 10.3934/dcdsb.2009.12.219

A remark on exponential stability of time-delayed Burgers equation

Yanbin Tang 1, and  Ming Wang 1,

1. 

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China, China

Received  November 2008 Revised  January 2009 Published  May 2009

In this paper, we consider the initial-boundary value problem of Burgers equation with a time delay. Using a fixed point theorem and a comparison principle, we show that the time-delayed Burgers equation is exponentially stable under small delays. The result is more explicit, but also complements, the result given by Weijiu Liu [Discrete and Continuous Dynamical Systems-Series B, 2:1(2002),47-56], which was based on the Liapunov function approach.
Keywords: Burgers equation, Fixed point theorem, Comparison principle., Time delay, Exponential stability.
Mathematics Subject Classification: Primary: 35R10, 35B35; Secondary: 35Q5.
Citation: Yanbin Tang, Ming Wang. A remark on exponential stability of time-delayed Burgers equation. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 219-225. doi: 10.3934/dcdsb.2009.12.219
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