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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 163070, 8 pages
http://dx.doi.org/10.1155/2013/163070
Research Article

Persistence Property and Asymptotic Description for DGH Equation with Strong Dissipation

Department of Basic, Zhejiang Dongfang Vocational Technical College, Wenzhou, Zhejiang 325011, China

Received 9 February 2013; Accepted 10 March 2013

Academic Editor: Yonghui Xia

Copyright © 2013 Ke-chuang Wang. 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 present work is mainly concerned with the Dullin-Gottwald-Holm (DGH) equation with strong dissipation. We establish a sufficient condition to guarantee global-in-time solutions, then present persistence property for the Cauchy problem, and describe the asymptotic behavior of solutions for compactly supported initial data.