Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 777 - 809, Volume 15, Issue 3, July 2006      doi:10.3934/dcds.2006.15.777

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Igor Chueshov - Kharkov University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov, Ukraine (email)
Irena Lasiecka - University of Virginia, Department of Mathematics, Charlottesville, VA 22901, United States (email)

Abstract: 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: 34D35.

Received: March 2005;      Revised: August 2005;      Available Online: April 2006.