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 - <p>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.</p>