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

Igor Chueshov; Irena Lasiecka

doi:10.3934/dcds.2006.15.777

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2006, Volume 15, Issue 3: 777-809. Doi: 10.3934/dcds.2006.15.777

This issue Previous Article Non-autonomous boundary value problems on the real line Next Article Hyperbolic invariant sets with positive measures

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
2.
University of Virginia, Department of Mathematics, Charlottesville, VA 22901

Received: February 28, 2005

Revised: July 31, 2005

Published: August 2006

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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.

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Mathematics Subject Classification: Primary: 60H25, 47H10; Secondary: 34D35.

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

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