E (2010) Null controllability and stabilization of a linear Kuramoto-Sivashinsky equation

(Communicated by Yacine Chitour) Abstract. In this article, we study the boundary controllability of the linear Kuramoto-Sivashinsky equation on a bounded interval. The control acts on the first spatial derivative at the left endpoint. First, we prove that this control system is null controllable. It is done using a spectral analysis and the method of moments. Then, we introduce a boundary feedback law stabilizing to zero the solution of the closed-loop system. 1. Introduction and main results. The Kuramoto-Sivashinsky (KS) equation reads as yt + yxxxx + λyxx + yyx = 0, (1) where the real number λ> 0 is called the “anti-diffusion ” parameter. This equation was derived independently by Kuramoto et al. in [17, 18, 16] as a model for phas