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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| Language: | English |
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Wiley
2013-01-01
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| 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. |
| format | Article |
| id | doaj-art-e5a6b3600b8b42239adcb8cf1b5e8815 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT xiufangliu exponentialstabilizationfortimoshenkobeamwithdistributeddelayintheboundarycontrol AT genqixu exponentialstabilizationfortimoshenkobeamwithdistributeddelayintheboundarycontrol |