Geodesic
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

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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.

DOI : 10.1051/cocv:2005028
Classification : 35Q99, 74F99, 35B40
Keywords: distributed systems, boundary control, stabilization, exact controllability 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv:2005028/}
}
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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

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