A remark on exponential stability of time-delayed burgers equation

Abstract

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:l(2002),47-56], which was based on the Liapunov function approach.