EXISTENCE OF THE GENERALIZED EXPONENTIAL ATTRACTOR FOR COUPLED SUSPENSION BRIDGE EQUATIONS WITH DOUBLE NONLOCAL TERMS

Lulu Wang; Qiaozhen Ma

doi:10.11948/20230381

2024 Volume 14 Issue 4

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Lulu Wang, Qiaozhen Ma. EXISTENCE OF THE GENERALIZED EXPONENTIAL ATTRACTOR FOR COUPLED SUSPENSION BRIDGE EQUATIONS WITH DOUBLE NONLOCAL TERMS[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2337-2358. doi: 10.11948/20230381

Citation:

Lulu Wang, Qiaozhen Ma. EXISTENCE OF THE GENERALIZED EXPONENTIAL ATTRACTOR FOR COUPLED SUSPENSION BRIDGE EQUATIONS WITH DOUBLE NONLOCAL TERMS[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2337-2358. doi: 10.11948/20230381

EXISTENCE OF THE GENERALIZED EXPONENTIAL ATTRACTOR FOR COUPLED SUSPENSION BRIDGE EQUATIONS WITH DOUBLE NONLOCAL TERMS

Lulu Wang^1,,
Qiaozhen Ma^1,2, ,

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
2.
Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou, Gansu 730070, China

Author Bio: Email: wangll0526@126.com (L. Wang)
Corresponding author: Email: maqzh@nwnu.edu.cn(Q. Ma)
Fund Project: The authors were supported by the National Natural Science Foundation of China (Grant No. 11961059, 12101502)

Abstract

Abstract

We investigate the long-time dynamical behavior of coupled suspension bridge equations with double nonlocal terms by using the quasi-stable methods. We first establish the well-posedness of the solutions by means of the monotone operator theory. Secondly, the dissipation of solution semigroup $ \{S(t)\}_{t\geq0} $ is obtained, and then, the asymptotic smoothness of solution semigroup $ \{S(t)\}_{t\geq0} $ is verified by the energy reconstruction method; ultimately, we prove the existence of global attractor. Finally, we show the existence of the generalized exponential attractor.
- Coupled suspension bridge equations /
- double nonlocal terms /
- global attractor /
- generalized exponential attractor
MSC: 35B40, 35B41

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References

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