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• W2927094162 abstract "The aim of this paper is to study the controllability and stabilization for the Benjamin equation on a periodic domain $mathbb{T}$. We show that the Benjamin equation is globally exactly controllable and globally exponentially stabilizable in $H_{p}^{s}(mathbb{T}),$ with $sgeq 0.$ First we prove propagation of compactness, propagation of regularity of solution in Bourgain's spaces and unique continuation property, and use them to obtain the global exponential stabilizability corresponding to a natural feedback law. Combining the global exponential stability and the local controllability result we prove the global controllability as well. Also, we prove that the closed-loop system with a different feedback control law is locally exponentially stable with an arbitrary decay rate. Finally, a time-varying feedback law is designed to guarantee a global exponential stability with an arbitrary decay rate. The results obtained here extend the ones we proved for the linearized Benjamin equation in cite{Vielma and Panthee}." @default.
• W2927094162 created "2019-04-11" @default.
• W2927094162 creator A5015969170 @default.
• W2927094162 creator A5076546134 @default.
• W2927094162 date "2019-04-06" @default.
• W2927094162 modified "2023-09-23" @default.
• W2927094162 title "On the controllability and Stabilization of the Benjamin Equation" @default.
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• W2927094162 hasPublicationYear "2019" @default.
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