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August  2006, 15(3): 777-809. doi: 10.3934/dcds.2006.15.777

Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models

Igor Chueshov 1, and  Irena Lasiecka 2,

1. 

Kharkov University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov, Ukraine
2. 

University of Virginia, Department of Mathematics, Charlottesville, VA 22901

Received  March 2005 Revised  August 2005 Published  April 2006

We study dynamics of a class of nonlinear Kirchhoff-Boussinesq plate models. The main results of the paper are: (i) existence and uniqueness of weak (finite energy) solutions, (ii) existence of weakly compact attractors.
Keywords: 2D Boussinesq models, weak well-posedness, global attractors..
Mathematics Subject Classification: Primary: 60H25, 47H10; Secondary: 34D3.
Citation: Igor Chueshov, Irena Lasiecka. Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 777-809. doi: 10.3934/dcds.2006.15.777
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