Exponential stability and numerical treatment for piezoelectric beams with magnetic effect

In this paper, we consider a one-dimensional dissipative system of piezoelectric beams with magnetic effect, inspired by the model studied by Morris and Özer (Proc. of 52nd IEEE Conference on Decision & Control (2013) 3014–3019). Our main interest is to analyze the issues relating to exponential...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2018-01, Vol.52 (1), p.255-274
Main Authors: Ramos, Anderson J.A., Gonçalves, Cledson S.L., Corrêa Neto, Silvério S.
Format: Article
Language:English
Subjects:
35L53
65M06
Decision analysis
exponential decay
finite-difference discretization
magnetic effect
Magnetic effects
Mathematical models
Piezoelectric beams
Piezoelectricity
Stability analysis
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Summary:In this paper, we consider a one-dimensional dissipative system of piezoelectric beams with magnetic effect, inspired by the model studied by Morris and Özer (Proc. of 52nd IEEE Conference on Decision & Control (2013) 3014–3019). Our main interest is to analyze the issues relating to exponential stability of the total energy of the continuous problem and reproduce a numerical counterpart in a totally discrete domain, which preserves the important decay property of the numerical energy.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2018004