Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 269, Issue 2, Pages 556-577Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/S0022-247X(02)00036-7
Keywords
Timoshenko beam; boundary feedback; C-0-semigroups; asymptotic stability; exponential stability
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This paper is concerned with the stabilization problem of Timoshenko beam in the presence of linear dissipative boundary feedback controls. Using C-0-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 asymptoic stability for the closed loop system. (C) 2002 Elsevier Science (USA). All rights reserved.
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