Asymptotic Behavior of Solutions for the Time-Delayed Kuramoto-Sivashinsky Equation

Abstract

In this paper, we investigate the asymptotic behavior of the solutions for the Kuramoto-Sivashinsky equation with a time delay. We prove the global existence of solutions and energy decay. By using the Liapunov function method, we shall show that the solution is exponentially decay if the delay parameter $\tau$ is sufficiently small.