@article{Liu2025, 
author = {Yang Liu and Xiao Long and Li Zhang},
title = {Long-time dynamics for a coupled system modeling the oscillations of suspension bridges},
year = {2025},
journal = {Communications in Analysis and Mechanics},
volume = {17},
number = {1},
pages = {15-40},
keywords = {coupled beam-string system, global well-posedness, global attractors, gradient dynamical system, quasi-stability},
url = {https://www.sciopen.com/article/10.3934/cam.2025002},
doi = {10.3934/cam.2025002},
abstract = {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.}
}