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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2015

Control and Stabilization of the Benjamin-Ono Equation on a Periodic Domain

Résumé

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 in 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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Dates et versions

hal-00734445 , version 1 (22-09-2012)

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Felipe Linares, Lionel Rosier. Control and Stabilization of the Benjamin-Ono Equation on a Periodic Domain. Transactions of the American Mathematical Society, 2015, 367 (7), pp.4595-4626. ⟨hal-00734445⟩
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