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October  2010, 26(4): 1441-1469. doi: 10.3934/dcds.2010.26.1441

Asymptotic behaviour of the Darcy-Boussinesq system at large Darcy-Prandtl number

Rana D. Parshad 1,

1. 

Florida State University, Department of Mathematics, Tallahassee, FL 32306, United States

Received  November 2008 Revised  May 2009 Published  December 2009

We study asymptotic behavior of the Darcy-Boussinesq system at large Darcy-Prandtl number. We prove that the global attractors for this system converge to that of the infinite Darcy-Prandtl number model. We also show the convergence of statistical properties including invariant measures.
Keywords: Global Attractor, Darcy-Prandtl Number, Darcy-Boussinesq system, Singular Perturbation., Invariant Measures.
Mathematics Subject Classification: Primary: 35B40, 35B41, 37L40; Secondary: 76S05, 76R1.
Citation: Rana D. Parshad. Asymptotic behaviour of the Darcy-Boussinesq system at large Darcy-Prandtl number. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1441-1469. doi: 10.3934/dcds.2010.26.1441
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