Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay
Abstract
:1. Introduction
- Study the stability of the Kirchhoff plate equation in the presence of a damping term and a time delay term (of linear or fractional type) that have different orders (as carried out in the very recent work [24] for wave equations), which is not the case for all previous works, even for wave equations and other damped systems, where the damping and the time delay terms are of the same orders.
- Prove the exponential decay of the energy of our model, which is not the case in the presence of frictional damping.
2. Exponential Stability of System (1) in the Case Without Delay
3. Exponential Stability of System (1) in the Case with Linear Delay
4. Exponential Stability of System (1) in the Case with Fractional Delay
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Hajjej, Z.; Zhang, H. Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay. Symmetry 2024, 16, 1427. https://doi.org/10.3390/sym16111427
Hajjej Z, Zhang H. Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay. Symmetry. 2024; 16(11):1427. https://doi.org/10.3390/sym16111427
Chicago/Turabian StyleHajjej, Zayd, and Hongwei Zhang. 2024. "Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay" Symmetry 16, no. 11: 1427. https://doi.org/10.3390/sym16111427
APA StyleHajjej, Z., & Zhang, H. (2024). Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay. Symmetry, 16(11), 1427. https://doi.org/10.3390/sym16111427