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

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  • 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 $(H^{2}(\Omega )\cap H_{0}^{1}(\Omega ))\times H_{0}^{1}(\Omega )$.
    Mathematics Subject Classification: 35B41, 35L05, 35L75.

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