Communications in Information and Systems
Volume 12 (2012)
Control and stabilization of the Kawahara equation on a periodic domain
Pages: 77 – 96
In this paper, we study a class of distributed parameter control system described by the Kawahara equation posed on a periodic domain $T$ (a unit circle in the plane) with an internal control acting on an arbitrary small nonempty subdomain of $T$. Aided by the Bourgain smoothing property of the Kawahara equation on a periodic domain, we show that the system is locally exactly controllable and exponentially stabilizable with an arbitrarily large decay rate.
Kawahara equation, well-posedness, exact controllability, feedback control, stabilizability
2010 Mathematics Subject Classification
35Q53, 93B05, 93D15