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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 714696, 19 pages
http://dx.doi.org/10.1155/2012/714696
Research Article

Strong Uniform Attractors for Nonautonomous Suspension Bridge-Type Equations

College of Mathematics and Statistics, Northwest Normal University, Gansu, Lanzhou 730070, China

Received 6 September 2012; Accepted 23 October 2012

Academic Editor: Carlo Cattani

Copyright © 2012 Xuan Wang and Qiaozhen Ma. 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

We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert space , where the nonlinearity is translation compact and the time-dependent external forces only satisfy condition ( ) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.