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Mathematical Problems in Engineering
Volume 2015, Article ID 857920, 10 pages
http://dx.doi.org/10.1155/2015/857920
Research Article

Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions

1Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
2Department of Mathematics, Taiyuan University of Science and Technology, Taiyuan 030024, China

Received 12 December 2014; Revised 11 January 2015; Accepted 13 January 2015

Academic Editor: Mohamed Abd El Aziz

Copyright © 2015 Danxia Wang 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

Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.