Well-posedness and longtime behaviour of a coupled nonlinear system modeling a suspension bridge

Abstract

In this paper we discuss the well-posedness and the asymptotic behavior of a doubly nonlinear problem describing the vibrations of a Kelvin–Voigt string–beam system which models a suspension bridge. For this model we obtain the existence and uniqueness of solutions and the exponential stability of the homogeneous system, provided that the constant axial force \(p\) is smaller than a critical value. For a general \(p,\) the existence of the regular global attractor is proved when the external loads are independent of time.