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February, 2019 Well-posedness and Stability of Two Classes of Plate Equations with Memory and Strong Time-dependent Delay
Baowei Feng, Gongwei Liu
Taiwanese J. Math. 23(1): 159-192 (February, 2019). DOI: 10.11650/tjm/180801

Abstract

Two classes of plate equations with past history and strong time-dependent delay in the internal feedback are considered. Our results contain the global well-posedness and exponential stability of the two systems. We prove the global well-posedness of a system with rotational inertia without any restrictions on $\mu_1$, $\mu_2$, and the system without rotational inertia under the assumption $|\mu_2| \leq \mu_1$. For the system with rotational inertia, we establish exponential stability to the plate equation with the memory term only to control the delay term if the amplitude of the time delay term is small, and the stability result also holds for the plate equation with strong anti-damping. For the system without rotational inertia, we obtain the exponential stability under the assumption $|\mu_2| \lt \sqrt{1-d} \mu_1$.

Citation

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Baowei Feng. Gongwei Liu. "Well-posedness and Stability of Two Classes of Plate Equations with Memory and Strong Time-dependent Delay." Taiwanese J. Math. 23 (1) 159 - 192, February, 2019. https://doi.org/10.11650/tjm/180801

Information

Received: 20 April 2018; Revised: 3 July 2018; Accepted: 31 July 2018; Published: February, 2019
First available in Project Euclid: 10 August 2018

zbMATH: 07021723
MathSciNet: MR3909995
Digital Object Identifier: 10.11650/tjm/180801

Subjects:
Primary: 35B40, 74Dxx, 93D15, 93D20

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 1 • February, 2019
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