| Issue |
ESAIM: M2AN
Volume 52, Number 1, January–February 2018
|
|
|---|---|---|
| Page(s) | 255 - 274 | |
| DOI | https://doi.org/10.1051/m2an/2018004 | |
| Published online | 04 May 2018 | |
Exponential stability and numerical treatment for piezoelectric beams with magnetic effect★
1
PhD Program in Mathematics, Federal University of Pará,
Augusto Corrêa Street 01,
66075-110,
Belém,
PA, Brazil
2
Interdisciplinary Innovation Laboratory (LabX), Faculty of Mathematics, Federal University of Pará,
Salinópolis,
PA, Brazil
* Corresponding author: ramos@ufpa.br
Received:
13
December
2016
Accepted:
11
January
2018
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.
Mathematics Subject Classification: 35L53 / 65M06
Key words: Piezoelectric beams, magnetic effect, exponential decay, finite-difference discretization
© EDP Sciences, SMAI 2018
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