Exact controllability of the Euler-Bernoulli equation with $L_{2}(\Sigma)$-control only in the Dirichlet Boundary condition

Lasiecka, I.; Triggiani, R.

Exact controllability of the Euler-Bernoulli equation with

L_{2}(\Sigma)

-control only in the Dirichlet Boundary condition

Lasiecka, I. ; Triggiani, R.

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 82 (1988), p. 35-42 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

The paper studies the problem of exact controllability of the Euler- Bernoulli equation in a cylinder $\Omega\times\left[0,T\right]$ of $\mathbb{R}^{n+1}$ , via boundary controls acting on its lateral surface.

Si danno condizioni per la controllabilità esatta dell'equazione di Bernoulli $w_{tt}+\Delta^{2}w=0$ in un cilindro di $\mathbb{R}^{n+1}$ mediante controlli sulla superficie laterale.

Publié le : 1988-03-01

MR 0999836 | Zbl 0666.49011 0648.35001

@article{RLINA_1988_8_82_1_35_0,
     author = {I. Lasiecka and R. Triggiani},
     title = {Exact controllability of the Euler-Bernoulli equation with $L\_{2}(\Sigma)$-control only in the Dirichlet Boundary condition},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {82},
     year = {1988},
     pages = {35-42},
     zbl = {0666.49011 0648.35001},
     mrnumber = {0999836},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1988_8_82_1_35_0}
}

Lasiecka, I.; Triggiani, R. Exact controllability of the Euler-Bernoulli equation with $L_{2}(\Sigma)$-control only in the Dirichlet Boundary condition. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 82 (1988) pp. 35-42. http://gdmltest.u-ga.fr/item/RLINA_1988_8_82_1_35_0/

Bibliographie

[B.-L.-R.1] Bardos, C., Lebeau, G. and Rauch, R. - Contrôle et stabilisation de l'equation des ondes. | Zbl 0644.49025

[G.1] Grisvard, P. (1967) - Caracterisation de quelques espaces d'interpolation, «Arch. Rat. Mech. Anal.», 25, 40-63. | MR 213864 | Zbl 0187.05901

[K.1] Komornik, V. (1987) - Controlabilité exacte en un temps minimal, CRAS Paris, t. 304, Serie 1, n° 9. | MR 883479 | Zbl 0611.49027

[L.1] Lions, J.L. (1986) - Exact controllability, stabilization and perturbations, J. von Neumann Lecture, July. | Zbl 0644.49028

[L.2] Lions, J.L., Paper dedicated to Mizohata.

[L.-T.1] Lasiecka, I. and Triggiani, R. - Exact controllability for Euler-Bernoulli equations with controls in the Dirichlet and Neumann boundary conditions: a non-conservative case, «SIAM J. Control & Optimiz.», to appear. | MR 984832 | Zbl 0666.49013

[L.-T.2] Lasiecka, I. and Triggiani, R. (1986) - Exact controllability for the wave equation with Neumann boundary control, «Applied Mathem. and Optimiz.», to appear. | MR 974187 | Zbl 0666.49012

[T.1] Triggiani, R. (1986) - Exact boundary controllability on $L^{2}(\Omega)\times H^{-1}(\Omega)$ for the wave equation with Dirichlet control acting on a portion of the boundary, and related problems, «Applied Mathem. and Optiming.», to appear. | MR 945765 | Zbl 0656.93011

[Z.1] Zuazua, E., Controlabilité exacte d'un modèle de plaques vibrantes en un temps arbitrairement petit, CRAS Paris, 1. 304, Serie I, n. 7, 1987. | MR 880573 | Zbl 0611.49028