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Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control

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  • Xiu Fang Liu
  • Gen Qi Xu

Abstract

We consider the exponential stabilization for Timoshenko beam with distributed delay in the boundary control. Suppose that the controller outputs are of the form α1u1(t)+β1u1(t-τ)+∫-τ0 g1(η)u1(t+η)dη and α2u2(t)+β2u2(t-τ)+∫-τ0 g2(η)u2(t+η)dη; where u1(t) and u2(t) are the inputs of boundary controllers. In the past, most stabilization results for wave equations and Euler‐Bernoulli beam with delay are required αi > βi > 0, i = 1,2. In the present paper, we will give the exponential stabilization about Timoshenko beam with distributed delay and demand to satisfy the lesser conditions for αi, βi, i = 1,2.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:726794
DOI: 10.1155/2013/726794
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