Global attractors for strongly damped waveequations with displacement dependent damping and nonlinear source term ofcritical exponent

A. Kh. Khanmamedov

doi:10.3934/dcds.2011.31.119

Article Contents

2011, Volume 31, Issue 1: 119-138. Doi: 10.3934/dcds.2011.31.119

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Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

A. Kh. Khanmamedov^1,

1.
Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06800, Ankara

Received: February 28, 2010

Revised: November 30, 2010

Published: December 2010

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Abstract

In this paper the long time behaviour of the solutions of the 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in $H_{0}^{1}(\Omega )\times L_{2}(\Omega )$ and then it is proved that this is also a global attractor in $(H^{2}(\Omega )\cap H_{0}^{1}(\Omega ))\times H_{0}^{1}(\Omega )$.

Keywords:

Attractors,
strongly damped wave equations.

Mathematics Subject Classification: 35B41, 35L05, 35L75.

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