Asymptotic behavior of Timoshenko beam with dissipative boundary feedback |
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| Authors: | Qing-Xu YanShui-Hung Hou De-Xing Feng |
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| Institution: | a Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
b Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China |
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| Abstract: | This paper is concerned with the stabilization problem of Timoshenko beam in the presence of linear dissipative boundary feedback controls. Using C0-semigroups theory we establish the existence and the uniqueness of solution of the proposed closed loop system. In order to consider the asymptotic behavior of the closed loop system, we first discuss the existence of nonzero solution of a closely related boundary value problem. Then we derive various necessary and sufficient conditions for the system to be asymptotically stable. Finally, we prove the equivalence between the exponential stability and the asymptotic stability for the closed loop system. |
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| Keywords: | Timoshenko beam Boundary feedback C0-semigroups Asymptotic stability Exponential stability |
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