CPAA
Long-time behaviour of doubly nonlinear parabolic equations
A. Kh. Khanmamedov
Communications on Pure & Applied Analysis 2009, 8(4): 1373-1400 doi: 10.3934/cpaa.2009.8.1373
We consider a doubly nonlinear parabolic equation in $R^n$. Under suitable hypotheses we prove that a semigroup generated by this equation possesses a global attractor.
keywords: nonlinear parabolic equations. Attractors
DCDS
Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent
A. Kh. Khanmamedov
Discrete & Continuous Dynamical Systems - A 2011, 31(1): 119-138 doi: 10.3934/dcds.2011.31.119
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.
DCDS
Long-time behaviour of wave equations with nonlinear interior damping
A. Kh. Khanmamedov
Discrete & Continuous Dynamical Systems - A 2008, 21(4): 1185-1198 doi: 10.3934/dcds.2008.21.1185
We prove the existence of attractors for higher dimensional wave equations with nonlinear interior damping which grows faster than polynomials at infinity.
keywords: Attractors wave equations.

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