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Chueshov, I. and Rezounenko, A. (2015) Finite-dimensional Global Attractors for Parabolic Nonlinear Equations with State-dependent Delay. Communications on Pure and Applied Analysis, 14, 1685-1704.
https://doi.org/10.3934/cpaa.2015.14.1685

has been cited by the following article:

• TITLE: Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay

  AUTHORS: Suping Wang, Qiaozhen Ma, Xukui Shao

  KEYWORDS: Suspension Bridge Equation, State-Dependent Delay, Global Attractor, Exponential Attractor, Quasi-Stability

  JOURNAL NAME: Engineering, Vol.15 No.10, October 31, 2023

  ABSTRACT: This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.