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Zbl 1222.35040
Khanmamedov, A.Kh.
Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent. (English)
[J] Discrete Contin. Dyn. Syst. 31, No. 1, 119-138 (2011). ISSN 1078-0947; ISSN 1553-5231/e

Summary: 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 $(H^{2}(\Omega ) \cap H_{0}^{1}(\Omega )) \times H_{0}^{1}(\Omega )$.

MSC 2000:: *35B41 Attractors
35L05 Wave equation
35L75 Nonlinear hyperbolic PDE of higher $(>2)$ order

Keywords: attractors; strongly damped wave equations

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