Global attractors for a nonlinear plate equation modeling the oscillations of suspension bridges

Yang Liu; Yang Liu

doi:10.3934/cam.2023021

Communications in Analysis and Mechanics

2023, Volume 15, Issue 3: 436-456. doi: 10.3934/cam.2023021

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Research article

Global attractors for a nonlinear plate equation modeling the oscillations of suspension bridges

Yang Liu ^{1,2
,
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1.
College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
2.
College of Mathematics, Sichuan University, Chengdu 610065, China

Received: 18 May 2023 Revised: 28 June 2023 Accepted: 28 June 2023 Published: 17 July 2023
35L35, 35A01, 35B41

This paper is concerned with a nonlinear plate equation modeling the oscillations of suspension bridges. Under mixed boundary conditions consisting of simply supported and free boundary conditions, we obtain the global well-posedness of solutions in suitable function spaces. In addition, we use the perturbed energy method to prove the existence of a bounded absorbing set and establish a stabilizability estimate. Then, we derive the existence of a global attractor by verifying the asymptotic smoothness of the corresponding dissipative dynamical system.
- nonlinear plate equations,
- global well-posedness,
- global attractors,
- dissipative dynamical system,
- asymptotic smoothness
Citation: Yang Liu. Global attractors for a nonlinear plate equation modeling the oscillations of suspension bridges[J]. Communications in Analysis and Mechanics, 2023, 15(3): 436-456. doi: 10.3934/cam.2023021

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Abstract

This paper is concerned with a nonlinear plate equation modeling the oscillations of suspension bridges. Under mixed boundary conditions consisting of simply supported and free boundary conditions, we obtain the global well-posedness of solutions in suitable function spaces. In addition, we use the perturbed energy method to prove the existence of a bounded absorbing set and establish a stabilizability estimate. Then, we derive the existence of a global attractor by verifying the asymptotic smoothness of the corresponding dissipative dynamical system.

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