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

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

Pages: 119 - 138, Volume 31, Issue 1, September 2011      doi:10.3934/dcds.2011.31.119

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A. Kh. Khanmamedov - Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06800, Ankara, Turkey (email)

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.

Received: March 2010;      Revised: December 2010;      Available Online: June 2011.