Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain | Zendy

Xia Zhao | Zendy; Meng Bai | Zendy

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Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain

Author(s) -

Xia Zhao,

Meng Bai

Publication year - 2018

Publication title -

journal of partial differential equations

Language(s) - English

Resource type - Journals

eISSN - 2079-732X

pISSN - 1000-940X

DOI - 10.4208/jpde.v31.n1.3

Subject(s) - korteweg–de vries equation , domain (mathematical analysis) , order (exchange) , control (management) , control theory (sociology) , mathematics , mathematical analysis , computer science , physics , economics , artificial intelligence , nonlinear system , finance , quantum mechanics

In this paper, we study exact controllability and feedback stabilization for the distributed parameter control system described 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. AMS Subject Classifications: 93B05, 93D15, 35Q53 Chinese Library Classifications: O175.2, O175.4, O29

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