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.
Mots clés : Piezoelectric beams, magnetic effect, exponential decay, finite-difference discretization
@article{M2AN_2018__52_1_255_0, author = {Ramos, Anderson J.A. and Gon\c{c}alves, Cledson S.L. and Corr\^ea Neto, Silv\'erio S. }, title = {Exponential stability and numerical treatment for piezoelectric beams with magnetic effect}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {255--274}, publisher = {EDP-Sciences}, volume = {52}, number = {1}, year = {2018}, doi = {10.1051/m2an/2018004}, zbl = {1398.35232}, mrnumber = {3808160}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2018004/} }
TY - JOUR AU - Ramos, Anderson J.A. AU - Gonçalves, Cledson S.L. AU - Corrêa Neto, Silvério S. TI - Exponential stability and numerical treatment for piezoelectric beams with magnetic effect JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 255 EP - 274 VL - 52 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2018004/ DO - 10.1051/m2an/2018004 LA - en ID - M2AN_2018__52_1_255_0 ER -
%0 Journal Article %A Ramos, Anderson J.A. %A Gonçalves, Cledson S.L. %A Corrêa Neto, Silvério S. %T Exponential stability and numerical treatment for piezoelectric beams with magnetic effect %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 255-274 %V 52 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2018004/ %R 10.1051/m2an/2018004 %G en %F M2AN_2018__52_1_255_0
Ramos, Anderson J.A.; Gonçalves, Cledson S.L.; Corrêa Neto, Silvério S. . Exponential stability and numerical treatment for piezoelectric beams with magnetic effect. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 1, pp. 255-274. doi : 10.1051/m2an/2018004. http://www.numdam.org/articles/10.1051/m2an/2018004/
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