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

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)+∫-τ0‍g1(η)u1(t+η)dη and α2u2(t)+β2u2(t-τ)+∫-τ0‍g2(η)u2(t+η)dη; where u1(t) and u2(t) are the inputs of boundary controll...

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Main Authors: Xiu Fang Liu, Gen Qi Xu
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/726794
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author Xiu Fang Liu
Gen Qi Xu
author_facet Xiu Fang Liu
Gen Qi Xu
author_sort Xiu Fang Liu
collection DOAJ
description 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)+∫-τ0‍g1(η)u1(t+η)dη and α2u2(t)+β2u2(t-τ)+∫-τ0‍g2(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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institution Kabale University
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language English
publishDate 2013-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-e5a6b3600b8b42239adcb8cf1b5e88152025-02-03T05:46:11ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/726794726794Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary ControlXiu Fang Liu0Gen Qi Xu1Department of Mathematics, Tianjin University, Tianjin 300072, ChinaDepartment of Mathematics, Tianjin University, Tianjin 300072, ChinaWe 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)+∫-τ0‍g1(η)u1(t+η)dη and α2u2(t)+β2u2(t-τ)+∫-τ0‍g2(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.http://dx.doi.org/10.1155/2013/726794
spellingShingle Xiu Fang Liu
Gen Qi Xu
Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control
Abstract and Applied Analysis
title Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control
title_full Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control
title_fullStr Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control
title_full_unstemmed Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control
title_short Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control
title_sort exponential stabilization for timoshenko beam with distributed delay in the boundary control
url http://dx.doi.org/10.1155/2013/726794
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AT genqixu exponentialstabilizationfortimoshenkobeamwithdistributeddelayintheboundarycontrol