Abstract
In this paper, we first establish a criterion based on contractive function for the existence of generalized polynomial attractors. This criterion only involves some rather weak compactness associated with the repeated inferior limit and requires no compactness, which makes it suitable for critical cases. Then by this abstract theorem, we verify the existence of a generalized polynomial attractor and estimate its attractive speed for the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity.
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