Geodesic
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

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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.

DOI : 10.1051/m2an/2018004
Classification : 35L53, 65M06
Keywords: Piezoelectric beams, magnetic effect, exponential decay, finite-difference discretization

Ramos, Anderson J.A. 1 ; Gonçalves, Cledson S.L. 1 ; Corrêa Neto, Silvério S. 1

1 
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     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},
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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

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