Abstract
This work is devoted to the following nonlocal extensible beam equation with time delay: u t t + Δ 2 u − M ( ∫ Ω | ∇ u | 2 d x ) Δ u + a 0 u t ( x , t ) + a 1 u t ( x , t − τ ) + φ ( u ) = f , on a bounded smooth domain . The main purpose of this paper is to consider the long-time dynamics of the system. Under suitable assumptions, the quasi-stability property of the system is established, based on which the existence and regularity of a finite-dimensional compact global attractor are obtained. Moreover, the existence of exponential attractors is proved.
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