Open AccessStabilization of 2-d Mindlin-Timoshenko plates with localized acoustic boundary feedback
Author(s) -
Yubiao Liu,
Chunguo Zhang,
Tehuan Chen
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021006
Subject(s) - exponential stability , remainder , semigroup , mathematics , boundary (topology) , dirichlet boundary condition , polynomial , operator (biology) , mathematical analysis , domain (mathematical analysis) , boundary value problem , stability (learning theory) , computer science , nonlinear system , physics , arithmetic , repressor , quantum mechanics , machine learning , transcription factor , gene , biochemistry , chemistry
In this paper, we investigate the well-posedness and the asymptotic stability of a two dimensional Mindlin-Timoshenko plate imposed the so-called acoustic control by a part of the boundary and a Dirichlet boundary condition on the remainder. We first establish the well-posedness results of our model based on the theory of linear operator semigroup and then prove that the system is not exponentially stable by using the frequency domain approach. Finally, we show that the system is polynomially stable with the aid of the exponential or polynomial stability of a system with standard damping acting on a part of the boundary.