TY - JOUR T1 - Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain AU - Zhao , Xiangqing AU - Bai , Meng JO - Journal of Partial Differential Equations VL - 1 SP - 29 EP - 46 PY - 2018 DA - 2018/07 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n1.3 UR - https://global-sci.org/intro/article_detail/jpde/12510.html KW - High-order KdV equation KW - Bourgain smoothing property KW - exact controllability KW - Slemrod’s feedback law KW - exponential stabilizability AB -
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.