Open AccessApproximate controllability of nonsimple elastic plate with memory
Author(s) -
Moncef Aouadi,
Imed Mahfoudhi,
Taoufik Moulahi
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021147
Subject(s) - controllability , monotonic function , mathematics , constant (computer programming) , stability (learning theory) , mathematical analysis , computer science , machine learning , programming language
In this paper, we give some qualitative results on the behavior of a nonsimple elastic plate with memory corresponding to anti-plane shear deformations. First we describe briefly the equations of the considered plate and then we study the well-posedness of the resulting problem. Secondly, we perform the spectral analysis, in particular, we establish conditions on the physical constants of the plate to guarantee the simplicity and the monotonicity of the roots of the characteristic equation. The spectral results are used to prove the exponential stability of the solutions at an optimal decay rate given by the physical constants. Then we present an approximate controllability result of the considered control problem. Finally, we give some numerical experiments based on the spectral method developed with implementation in MATLAB for one and two-dimensional problems.