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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Main Authors: Yang Liu, Xiao Long, Li Zhang
Format: Article
Language:English
Published: AIMS Press 2025-01-01
Series:Communications in Analysis and Mechanics
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/cam.2025002
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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
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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