Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings

Gongwei Liu; Mengru Wang; Pengyan Ding; Gongwei Liu; Mengru Wang; Pengyan Ding

doi:10.3934/era.2022173

Electronic Research Archive

2022, Volume 30, Issue 9: 3397-3421. doi: 10.3934/era.2022173

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Research article

Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings

College of Science, Henan University of Technology, Zhengzhou 450001, China

Received: 24 March 2022 Revised: 24 June 2022 Accepted: 11 July 2022 Published: 19 July 2022

This paper is concerned with the long-time dynamical behavior of a piezoelectric system with magnetic effect, which has nonlinear damping terms and external forces with a parameter. At first, we use the nonlinear semigroup theory to prove the well-posedness of solutions. Then, we investigate the properties of global attractors and the existence of exponential attractors. Finally, the upper semicontinuity of global attractors has been investigated.
- piezoelectric system,
- the well posedness,
- global attractor,
- exponential attractors,
- upper semicontinuity of attractors
Citation: Gongwei Liu, Mengru Wang, Pengyan Ding. Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings[J]. Electronic Research Archive, 2022, 30(9): 3397-3421. doi: 10.3934/era.2022173

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Abstract

This paper is concerned with the long-time dynamical behavior of a piezoelectric system with magnetic effect, which has nonlinear damping terms and external forces with a parameter. At first, we use the nonlinear semigroup theory to prove the well-posedness of solutions. Then, we investigate the properties of global attractors and the existence of exponential attractors. Finally, the upper semicontinuity of global attractors has been investigated.

References

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