期刊
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 367, 期 7, 页码 4595-4626出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9947-2015-06086-3
关键词
Benjamin-Ono equation; periodic domain; unique continuation property; propagation of regularity; exact controllability; stabilization
类别
资金
- Agence Nationale de la Recherche [ANR-09-BLAN-0213-02]
- CNPq
- FAPERJ/Brazil
- Agence Nationale de la Recherche (ANR) [ANR-09-BLAN-0213] Funding Source: Agence Nationale de la Recherche (ANR)
It was proved by Linares and Ortega that the linearized Benjamin-Ono equation posed on a periodic domain T with a distributed control supported on an arbitrary subdomain is exactly controllable and exponentially stabilizable. The aim of this paper is to extend those results to the full Benjamin-Ono equation. A feedback law in the form of a localized damping is incorporated into the equation. A smoothing effect established with the aid of a propagation of regularity property is used to prove the semi-global stabilization in L-2(T) of weak solutions obtained by the method of vanishing viscosity. The local well-posedness and the local exponential stability in H-s(T) are also established for s > 1/2 by using the contraction mapping theorem. Finally, the local exact controllability is derived in H-s(T) for s > 1/2 by combining the above feedback law with some open loop control.
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