Global attractors for a nonlinear plate equation modeling the oscillations of suspension bridges

作者：Yang Liu · 发表于：Communications in Analysis and Mechanics · 年份：2023 · DOI：10.3934/cam.2023021 · 被引用次数：8 · 研究领域：Stability and Controllability of Differential Equations、Advanced Mathematical Modeling in Engineering、Navier-Stokes equation solutions

<abstract><p>This paper is concerned with a nonlinear plate equation modeling the oscillations of suspension bridges. Under mixed boundary conditions consisting of simply supported and free boundary conditions, we obtain the global well-posedness of solutions in suitable function spaces. In addition, we use the perturbed energy method to prove the existence of a bounded absorbing set and establish a stabilizability estimate. Then, we derive the existence of a global attractor by verifying the asymptotic smoothness of the corresponding dissipative dynamical system.</p></abstract>