Exact controllability of the Euler-Bernoulli equation with L 2 ⁢ ( Σ ) -control only in the Dirichlet Boundary condition

I. Lasiecka; R. Triggiani

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 1, page 35-42
  • ISSN: 1120-6330

Abstract

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The paper studies the problem of exact controllability of the Euler- Bernoulli equation in a cylinder Ω × [ 0 , T ] of ℝ n + 1 , via boundary controls acting on its lateral surface.

How to cite

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Lasiecka, I., and 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 Lincei. Matematica e Applicazioni 82.1 (1988): 35-42. <http://eudml.org/doc/287507>.

@article{Lasiecka1988,
abstract = {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.},
author = {Lasiecka, I., Triggiani, R.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Exact boundary controllability; Euler-Bernoulli equation; exact controllability; boundary controls},
language = {eng},
month = {3},
number = {1},
pages = {35-42},
publisher = {Accademia Nazionale dei Lincei},
title = {Exact controllability of the Euler-Bernoulli equation with $L_\{2\}(\Sigma)$-control only in the Dirichlet Boundary condition},
url = {http://eudml.org/doc/287507},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Lasiecka, I.
AU - Triggiani, R.
TI - Exact controllability of the Euler-Bernoulli equation with $L_{2}(\Sigma)$-control only in the Dirichlet Boundary condition
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/3//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 1
SP - 35
EP - 42
AB - 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.
LA - eng
KW - Exact boundary controllability; Euler-Bernoulli equation; exact controllability; boundary controls
UR - http://eudml.org/doc/287507
ER -

References

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  1. BARDOS, C., LEBEAU, G. and RAUCH, R. - Contrôle et stabilisation de l'equation des ondes. Zbl0644.49025
  2. GRISVARD, P. (1967) - Caracterisation de quelques espaces d'interpolation, «Arch. Rat. Mech. Anal.», 25, 40-63. Zbl0187.05901MR213864
  3. KOMORNIK, V. (1987) - Controlabilité exacte en un temps minimal, CRAS Paris, t. 304, Serie 1, n° 9. Zbl0611.49027MR883479
  4. LIONS, J.L. (1986) - Exact controllability, stabilization and perturbations, J. von Neumann Lecture, July. Zbl0644.49028
  5. LIONS, J.L., Paper dedicated to Mizohata. 
  6. 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. Zbl0666.49013MR984832DOI10.1137/0327018
  7. LASIECKA, I. and TRIGGIANI, R. (1986) - Exact controllability for the wave equation with Neumann boundary control, «Applied Mathem. and Optimiz.», to appear. Zbl0666.49012MR974187DOI10.1007/BF01448201
  8. TRIGGIANI, R. (1986) - Exact boundary controllability on L 2 ⁢ ( Ω ) × H - 1 ⁢ ( Ω ) for the wave equation with Dirichlet control acting on a portion of the boundary, and related problems, «Applied Mathem. and Optiming.», to appear. Zbl0656.93011MR945765DOI10.1007/BF01443625
  9. ZUAZUA, E., Controlabilité exacte d'un modèle de plaques vibrantes en un temps arbitrairement petit, CRAS Paris, 1. 304, Serie I, n. 7, 1987. Zbl0611.49028MR880573

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