Asymptotic behavior of solutions of time-delayed Burgers' equation

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. Wealso give an explicit estimate of the delay parameter in terms of the viscosityand initial conditions, which indicates that the delay parameter tends to zeroif the initial states tend to infinity or the viscosity tends to zero. Furthermore,we present numerical simulations for our theoretical results.