Volume 31, Issue 1
Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain

Xiangqing Zhao and Meng Bai

10.4208/jpde.v31.n1.3

J. Part. Diff. Eq., 31 (2018), pp. 29-46.

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  • Abstract

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.

  • History

Published online: 2018-07

  • AMS Subject Headings

93B05, 93D15, 35Q53

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