Volume 25, 2019
|Number of page(s)||14|
|Published online||18 October 2019|
Regularity and stability of coupled plate equations with indirect structural or Kelvin-Voigt damping
School of Mathematics, Tianjin University,
300354, PR China.
2 Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-3000, USA.
* Corresponding author: firstname.lastname@example.org
a This author is supported by the Natural Science Foundation of China grant NSFC-61573252.
Accepted: 4 November 2018
In this paper, the regularity and stability of the semigroup associated with a system of coupled plate equations is considered. Indirect structural or Kelvin-Voigt damping is imposed, i.e., only one equation is directly damped by one of these two damping. By the frequency domain method, we show that the associated semigroup of the system with indirect structural damping is analytic and exponentially stable. However, with the much stronger indirect Kelvin-Voigt damping, we prove that, by the asymptotic spectral analysis, the semigroup is even not differentiable. The exponential stability is still maintained. Finally, some numerical simulations of eigenvalues of the corresponding one-dimensional systems are also given.
Mathematics Subject Classification: 35Q74 / 74D05
Key words: Analyticity / structural damping / Kelvin-Voigt damping / exponential stability / semigroup / spectrum
© EDP Sciences, SMAI 2019
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