Long-time dynamics for a coupled system modeling the oscillations of suspension bridges

作者：Yang Liu, Xiao Long, Li Zhang · 发表于：Communications in Analysis and Mechanics · 年份：2025 · DOI：10.3934/cam.2025002 · 被引用次数：6 · 研究领域：Structural Engineering and Vibration Analysis、Vibration and Dynamic Analysis、Fluid Dynamics and Vibration Analysis

<p>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.</p>