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

Abstract

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.

Keywords

• nonlinear plate equations
• global well-posedness
• global attractors
• dissipative dynamical system
• asymptotic smoothness