Communications in Information and Systems

Volume 12 (2012)

Number 1

Control and stabilization of the Kawahara equation on a periodic domain

Pages: 77 – 96



Bing-Yu Zhang (Department of Mathematical Sciences, University of Cincinnati, Ohio, U.S.A.)

Xiangqing Zhao (Department of Mathematics, Zhejiang Ocean University, Zhejiang, China)


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

Published 18 March 2013