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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 5036048, 11 pages
http://dx.doi.org/10.1155/2016/5036048
Research Article

Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition

1School of Arts and Science, Sias International University, Zhengzhou 451150, China
2Wuhan Technology and Business University, Wuhan 430065, China

Received 29 November 2015; Accepted 7 February 2016

Academic Editor: Taher S. Hassan

Copyright © 2016 Fan Geng 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

The paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition . The main result is concerned with nonlinearities with supercritical growth. In that case, we construct a bounded absorbing set with further regularity and obtain quasi-stability estimates. Then the exponential attractor is established in natural energy space .