Long-time dynamics of a class of nonlocal extensible beams with time delay. (February 2022)

• Record Type: Journal Article
• Authors: Meng, Fengjuan; Liu, Cuncai; Zhang, Chang
• Is Part Of: Mathematics and mechanics of solids. Volume 27:Number 2(2022)
• Page Start: 319
• Page End: 333
• Publication Date: 2022-02
• Subjects: Extensible beam equation -- quasi-stability property -- time delay -- global attractor -- exponential attractor; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865211019457
• Languages: English
• ISSNs: 1081-2865

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 domainΩ ⊂ R n . 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.