Asymptotic Behavior of Solutions of Time-delayed Burgers’ Equation

In this paper, we consider the 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 term of the viscosity and the initial condition, which indicates that the delay parameter tends to zero if the initial state tends to infinity or the viscosity tends to zero. In our result, we do not impose any a priori boundedness assumption on the solution. Furthermore, we present numerical simulations for our theoretical results. AMS Subject Classification. 35R10, 35B35, 35Q53.