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Topological Methods in Nonlinear Analysis

Attractor for a model of extensible beam with damping on time-dependent space
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Attractor for a model of extensible beam with damping on time-dependent space

Authors

  • Fengjuan Meng
  • Yonghai Wang
  • Chunxiang Zhao

Keywords

Time-dependent, attractors, extensible beam equations, non-autonomous

Abstract

In this paper, we study the asymptotic behavior of the following extensible beam equations: $$ \varepsilon(t) u_{tt}+\Delta^2 u-M\bigg(\int_\Omega |\nabla u|^2dx\bigg) \Delta u +\alpha u_t+\varphi (u)=f, \quad t> \tau, $$ where $\varepsilon(t)$ is a decreasing function of time vanishing at infinity. After generalizing the abstract results on time dependent space, we establish an invariant time-dependent global attractor for the equation by proving the well-posedness (thereby, the existence of process), dissapativity and the compactness of the process. Our work supplements the theoretical results on time-dependent space and the results on the longtime behavior of the model.

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Published

2021-02-08

How to Cite

1.
MENG, Fengjuan, WANG, Yonghai and ZHAO, Chunxiang. Attractor for a model of extensible beam with damping on time-dependent space. Topological Methods in Nonlinear Analysis. Online. 8 February 2021. Vol. 57, no. 1, pp. 365 - 393. [Accessed 6 July 2025].
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