International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 725045, 21 pages
doi:10.1155/2011/725045
Research Article

Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity

1School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, Hunan, China
2Department of Mathematics and Science, Hunan First Normal University, Feng Lin San Lu 1015, Changsha 410205, Hunan, China
3School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, China

Received 20 December 2010; Accepted 23 February 2011

Academic Editor: Marco Squassina

Copyright © 2011 Zai-yun Zhang and Zhen-hai Liu. 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

We discuss global attractor for the generalized dissipative KDV equation with nonlinearity under the initial condition 𝑢 ( 𝑥 , 0 ) = 𝑢 0 ( 𝑥 ) . We prove existence of a global attractor in space 𝐻 2 ( Ω ) , by using decomposition method with cut-off function and Kuratowski 𝛼 -measure in order to overcome the noncompactness of the classical Sobolev embedding.