Regularity and stability of coupled plate equations with indirect structural or Kelvin-Voigt damping

¹ School of Mathematics, Tianjin University, Tianjin 300354, PR China.
² Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-3000, USA.

^* Corresponding author: zjhan@tju.edu.cn
^a This author is supported by the Natural Science Foundation of China grant NSFC-61573252.

Received: 6 December 2017
Accepted: 4 November 2018

Abstract

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.