Null controllability of a linear KdV equation on an interval with special boundary conditions

Abstract

In this paper, we deal with the null controllability of a linear Korteweg-de Vries equation with special boundary conditions. We first study the Cauchy problem and prove the existence and uniqueness of solutions in suitable spaces, and then prove the null controllability of this system by establishing an observability inequality which is proved with the help of a Carleman estimate.