Long-Term Damped Dynamics of the Extensible Suspension Bridge

Details Long-Term Damped Dynamics of the Extensible Suspension Bridge Long-Term Damped Dynamics of the Extensible Suspension Bridge

2011-02-04

arxiv.org/abs/1102.0877v1

International Journal of Differential Equations, Volume 2010, Article ID 383420, 19 pages

Physics

Mathematical Physics

19 pages, 1 figure

Scientific paper

10.1155/2010/383420

This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load p and stiffness k^2. For a general external source f, we prove the existence of bounded absorbing sets.When f is timeindependent, 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.

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