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March  2006, 16(1): 121-136. doi: 10.3934/dcds.2006.16.121

The global attractor of the damped, forced generalized Korteweg de Vries-Benjamin-Ono equation in $L^2$

1. 

Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088

2. 

Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

Received  May 2005 Revised  March 2006 Published  June 2006

The existence of the global attractor of the damped, forced generalized KdV-Benjamin-Ono equation in $L^2( \mathbb{R})$ is proved for forces in $L^2( \mathbb{R})$. Moreover, the global attractor in $L^2( \mathbb{R})$ is actually a compact set in $H^3( \mathbb{R})$.
Citation: Boling Guo, Zhaohui Huo. The global attractor of the damped, forced generalized Korteweg de Vries-Benjamin-Ono equation in $L^2$. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 121-136. doi: 10.3934/dcds.2006.16.121
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