Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain

Abstract

In this paper, we study exact controllability and feedback stabilization for the distributed parameter control systemdescribed by high-order KdV equation posed on a periodic domain T with an internal control acting on an arbitrary small nonempty subdomain ω of T. On one hand, we show that the distributed parameter control system is locally exactly controllable with the help of Bourgain smoothing effect; on the other hand, we prove that the feedback system is locally exponentially stable with an arbitrarily large decay rate when Slemrod’s feedback input is chosen.