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February  2002, 2(1): 47-56. doi: 10.3934/dcdsb.2002.2.47

Asymptotic behavior of solutions of time-delayed Burgers' equation

Weijiu Liu 1,

1. 

Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada

Received  March 2001 Revised  June 2001 Published  November 2001

In this paper, we consider Burgers' equation with a time delay. By using the Liapunov function method, we show that the delayed Burgers' equation is exponentially stable if the delay parameter is sufficiently small. We also give an explicit estimate of the delay parameter in terms of the viscosity and initial conditions, which indicates that the delay parameter tends to zero if the initial states tend to infinity or the viscosity tends to zero. Furthermore, we present numerical simulations for our theoretical results.
Keywords: stability, Liapunov function., Time delay, Burgers equation.
Mathematics Subject Classification: 35R10, 35B35, 35Q5.
Citation: Weijiu Liu. Asymptotic behavior of solutions of time-delayed Burgers' equation. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 47-56. doi: 10.3934/dcdsb.2002.2.47
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