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Uniform attractors for non-autonomous suspension bridge-type equations

Xuan Wang12*, Lu Yang2 and Qiaozhen Ma1

Author Affiliations

1 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, P.R. China

2 School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P.R. China

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Boundary Value Problems 2014, 2014:75  doi:10.1186/1687-2770-2014-75

Published: 28 March 2014


We discuss the long-time dynamical behavior of the non-autonomous suspension bridge-type equation, where the nonlinearity <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/75/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/75/mathml/M1">View MathML</a> is translation compact and the time-dependent external forces <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/75/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/75/mathml/M2">View MathML</a> only satisfy Condition (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/75/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/75/mathml/M3">View MathML</a>) instead of being translation compact. By applying some new results and the energy estimate technique, the existence of uniform attractors is obtained. The result improves and extends some known results.

MSC: 34Q35, 35B40, 35B41.

non-autonomous suspension bridge equation; uniform Condition (C); uniform attractor