Copyright © 2010 Ivana Bochicchio et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This work is focused on the doubly nonlinear equation ∂ttu+∂xxxxu+(p-∥∂xu∥L2(0,1)2)∂xxu+∂tu+k2u+=f, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k2. When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load p and stiffness k2. For a general external source f, we prove the existence of bounded absorbing sets. When f is time-independent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.