Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain (Journal of Partial Differential Equations, 2018)
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.
Keywords: High-order KdV equation; Bourgain smoothing property; exact controllability; Slemrod’s feedback law; exponential stabilizability