GLOBAL CONTROLLABILITY AND STABILIZABILITY OF KAWAHARA EQUATION ON A PERIODIC DOMAIN

In this paper we study controllability and stabilizability of a class of distributed parameter control system described by the Kawahara equation posed on a periodic domain T with internal control acting on a sub-domain w of T. Earlier in [42], aided by Bourgain smoothing property of the system, we showed that the system is locally exactly controllable and exponentially stabilizable. In this paper, helped further by certain properties of propagation of compactness and regularity in Bourgain spaces for the solutions of the associated linear system, we show that the system is globally exactly controllable and globally exponentially stabilizable.