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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 154102, 5 pages
http://dx.doi.org/10.1155/2013/154102
Research Article

Asymptotic Behavior of Global Solutions to the Boussinesq Equation in Multidimensions

School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Received 30 May 2013; Revised 16 September 2013; Accepted 20 September 2013

Academic Editor: Shaoyong Lai

Copyright © 2013 Yu-Zhu Wang and Qingnian Zhang. 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 Cauchy problem for the Boussinesq equation in multidimensions is investigated. We prove the asymptotic behavior of the global solutions provided that the initial data are suitably small. Moreover, our global solutions can be approximated by the solutions to the corresponding linear equation as time tends to infinity when the dimension of space .