Long-time dynamics for a coupled system modeling the oscillations of suspension bridges
This paper is concerned with a coupled system modeling the oscillations of suspension bridges, which consists of a beam equation and a viscoelastic string equation. We first transformed the original initial-boundary value problem into an equivalent one in the history space framework. Then we obtaine...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-01-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2025002 |
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| _version_ | 1850264998727647232 |
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| author | Yang Liu Xiao Long Li Zhang |
| author_facet | Yang Liu Xiao Long Li Zhang |
| author_sort | Yang Liu |
| collection | DOAJ |
| description | This paper is concerned with a coupled system modeling the oscillations of suspension bridges, which consists of a beam equation and a viscoelastic string equation. We first transformed the original initial-boundary value problem into an equivalent one in the history space framework. Then we obtained the global well-posedness and regularity of mild solutions by using the semigroup theory. In addition, we employed the perturbed energy method to establish a stabilizability estimate. By verifying the gradient property and quasi-stability of the corresponding dynamical system, we derived the existence of a global attractor with finite fractal dimension. |
| format | Article |
| id | doaj-art-326dee9495e2470592bbd15fed19e5b2 |
| institution | OA Journals |
| issn | 2836-3310 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj-art-326dee9495e2470592bbd15fed19e5b22025-08-20T01:54:34ZengAIMS PressCommunications in Analysis and Mechanics2836-33102025-01-01171154010.3934/cam.2025002Long-time dynamics for a coupled system modeling the oscillations of suspension bridgesYang Liu0Xiao Long1Li Zhang2College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, People's Republic of ChinaCollege of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, People's Republic of ChinaCollege of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, People's Republic of ChinaThis paper is concerned with a coupled system modeling the oscillations of suspension bridges, which consists of a beam equation and a viscoelastic string equation. We first transformed the original initial-boundary value problem into an equivalent one in the history space framework. Then we obtained the global well-posedness and regularity of mild solutions by using the semigroup theory. In addition, we employed the perturbed energy method to establish a stabilizability estimate. By verifying the gradient property and quasi-stability of the corresponding dynamical system, we derived the existence of a global attractor with finite fractal dimension.https://www.aimspress.com/article/doi/10.3934/cam.2025002coupled beam-string systemglobal well-posednessglobal attractorsgradient dynamical systemquasi-stability |
| spellingShingle | Yang Liu Xiao Long Li Zhang Long-time dynamics for a coupled system modeling the oscillations of suspension bridges Communications in Analysis and Mechanics coupled beam-string system global well-posedness global attractors gradient dynamical system quasi-stability |
| title | Long-time dynamics for a coupled system modeling the oscillations of suspension bridges |
| title_full | Long-time dynamics for a coupled system modeling the oscillations of suspension bridges |
| title_fullStr | Long-time dynamics for a coupled system modeling the oscillations of suspension bridges |
| title_full_unstemmed | Long-time dynamics for a coupled system modeling the oscillations of suspension bridges |
| title_short | Long-time dynamics for a coupled system modeling the oscillations of suspension bridges |
| title_sort | long time dynamics for a coupled system modeling the oscillations of suspension bridges |
| topic | coupled beam-string system global well-posedness global attractors gradient dynamical system quasi-stability |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2025002 |
| work_keys_str_mv | AT yangliu longtimedynamicsforacoupledsystemmodelingtheoscillationsofsuspensionbridges AT xiaolong longtimedynamicsforacoupledsystemmodelingtheoscillationsofsuspensionbridges AT lizhang longtimedynamicsforacoupledsystemmodelingtheoscillationsofsuspensionbridges |