We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control via a classical result due to Russell.
Mots clés : distributed systems, boundary control, stabilization, exact controllability
@article{COCV_2006__12_2_198_0, author = {Kapitonov, Boris and Miara, Bernadette and Menzala, Gustavo Perla}, title = {Stabilization of a layered piezoelectric {3-D} body by boundary dissipation}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {198--215}, publisher = {EDP-Sciences}, volume = {12}, number = {2}, year = {2006}, doi = {10.1051/cocv:2005028}, mrnumber = {2209350}, zbl = {1105.93047}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2005028/} }
TY - JOUR AU - Kapitonov, Boris AU - Miara, Bernadette AU - Menzala, Gustavo Perla TI - Stabilization of a layered piezoelectric 3-D body by boundary dissipation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 198 EP - 215 VL - 12 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2005028/ DO - 10.1051/cocv:2005028 LA - en ID - COCV_2006__12_2_198_0 ER -
%0 Journal Article %A Kapitonov, Boris %A Miara, Bernadette %A Menzala, Gustavo Perla %T Stabilization of a layered piezoelectric 3-D body by boundary dissipation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 198-215 %V 12 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2005028/ %R 10.1051/cocv:2005028 %G en %F COCV_2006__12_2_198_0
Kapitonov, Boris; Miara, Bernadette; Menzala, Gustavo Perla. Stabilization of a layered piezoelectric 3-D body by boundary dissipation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 2, pp. 198-215. doi : 10.1051/cocv:2005028. http://www.numdam.org/articles/10.1051/cocv:2005028/
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