NEW EXPLORATION ON APPROXIMATE CONTROLLABILITY OF DAMPED ELASTIC BEAM SYSTEMS IN BANACH SPACES

Haide Gou; Min Shi

doi:10.11948/20240335

2025 Volume 15 Issue 3

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Haide Gou, Min Shi. NEW EXPLORATION ON APPROXIMATE CONTROLLABILITY OF DAMPED ELASTIC BEAM SYSTEMS IN BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1674-1694. doi: 10.11948/20240335

Citation:

Haide Gou, Min Shi. NEW EXPLORATION ON APPROXIMATE CONTROLLABILITY OF DAMPED ELASTIC BEAM SYSTEMS IN BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1674-1694. doi: 10.11948/20240335

NEW EXPLORATION ON APPROXIMATE CONTROLLABILITY OF DAMPED ELASTIC BEAM SYSTEMS IN BANACH SPACES

Haide Gou^1, ,,
Min Shi^1,

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Author Bio: Email: 2409396161@qq.com(M. Shi)
Corresponding author: Email: 842204214@qq.com(H. Gou)
Fund Project: The authors were supported by National Natural Science Foundation of China (12061062), Lanzhou Youth Science and Technology Talent Innovation Project (grant No. 2023-QN-106), and Project of NWNU-LKQN2023-02, and Natural Science Foundation of Gansu Province (grant No. 24JRRA131, No. 24JRRA780)

Abstract

Abstract

This article mainly studies the existence and approximate controllability of mild solutions for a class of Volterra-Fredholm type integral-differential damped elastic beam systems in Banach spaces. Firstly, the existence of mild solutions was obtained using Banach fixed point theorem and operator semigroup theory. Secondly, we formalized and proved the sufficient conditions for the approximate controllability of our desired problem. To test the results of approximate controllability, we used sequence method without assuming that the corresponding linear system is approximately controllable. Finally, an example is given to illustrate the theory results.
- Approximate controllability /
- damped elastic beam systems /
- mild solutions /
- sequence method
MSC: 34K30, 34K35, 47H10, 93B05

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References

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