August  2007, 17(3): 509-528. doi: 10.3934/dcds.2007.17.509

Long-time asymptotic behavior of dissipative Boussinesq systems

1. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States

2. 

Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex

Received  October 2005 Revised  July 2006 Published  December 2006

In this paper, we study various dissipative mechanics associated with the Boussinesq systems which model two-dimensional small amplitude long wavelength water waves. We will show that the decay rate for the damped one-directional model equations, such as the KdV and BBM equations, holds for some of the damped Boussinesq systems.
Citation: Min Chen, Olivier Goubet. Long-time asymptotic behavior of dissipative Boussinesq systems. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 509-528. doi: 10.3934/dcds.2007.17.509
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