Long-Term Damped Dynamics of the Extensible Suspension Bridge

Ivana Bochicchio, Claudio Giorgi and Elena Vuk

International Journal of Differential Equations, 2010, vol. 2010, 1-19

Abstract:

This work is focused on the doubly nonlinear equation 𠜕 ð ‘¡ ð ‘¡ ð ‘¢ + 𠜕 ð ‘¥ ð ‘¥ ð ‘¥ ð ‘¥ ð ‘¢ + ( ð ‘ âˆ’ ‖ 𠜕 ð ‘¥ ð ‘¢ ‖ 2 ð ¿ 2 ( 0 , 1 ) ) 𠜕 ð ‘¥ ð ‘¥ ð ‘¢ + 𠜕 ð ‘¡ ð ‘¢ + 𠑘 2 ð ‘¢ + = ð ‘“ , whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness 𠑘 2 . When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load ð ‘ and stiffness 𠑘 2 . For a general external source ð ‘“ , we prove the existence of bounded absorbing sets. When ð ‘“ 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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:383420

DOI: 10.1155/2010/383420

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