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March  2009, 2(1): 37-53. doi: 10.3934/dcdss.2009.2.37

Long-time asymptotic behavior of two-dimensional dissipative Boussinesq systems

Min Chen 1, and  Olivier Goubet 2,

1. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907
2. 

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

Received  February 2008 Revised  July 2008 Published  January 2009

In this article, we consider the two-dimensional dissipative Boussinesq systems which model surface waves in three space dimensions. The long time asymptotics of the solutions for a large class of such systems are obtained rigorously for small initial data.
Keywords: dissipation, two-way propagation, Boussinesq systems, waves, long-time asymptotics..
Mathematics Subject Classification: Primary: 35Q35, 35Q53,76B15; Secondary: 65M7.
Citation: Min Chen, Olivier Goubet. Long-time asymptotic behavior of two-dimensional dissipative Boussinesq systems. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 37-53. doi: 10.3934/dcdss.2009.2.37
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