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2013 Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control
Xiu Fang Liu, Gen Qi Xu
Abstr. Appl. Anal. 2013(SI03): 1-15 (2013). DOI: 10.1155/2013/726794

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 α 1 u 1 ( t ) + β 1 u 1 ( t - τ ) + - τ 0 g 1 ( η ) u 1 ( t + η ) d η and α 2 u 2 ( t ) + β 2 u 2 ( t - τ ) + - τ 0 g 2 ( η ) u 2 ( t + η ) d η ; where u 1 ( t ) and u 2 ( t ) are the inputs of boundary controllers. In the past, most stabilization results for wave equations and Euler-Bernoulli beam with delay are required α i > β i > 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 α i , β i , i = 1,2 .

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Xiu Fang Liu. Gen Qi Xu. "Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control." Abstr. Appl. Anal. 2013 (SI03) 1 - 15, 2013. https://doi.org/10.1155/2013/726794

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095288
MathSciNet: MR3143567
Digital Object Identifier: 10.1155/2013/726794

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI03 • 2013
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