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 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.