Geometrical aspects of exact boundary controllability for the wave equation. A numerical study

M. Asch; G. Lebeau

ESAIM: Control, Optimisation and Calculus of Variations (1998)

  • Volume: 3, page 163-212
  • ISSN: 1292-8119

How to cite

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Asch, M., and Lebeau, G.. "Geometrical aspects of exact boundary controllability for the wave equation. A numerical study." ESAIM: Control, Optimisation and Calculus of Variations 3 (1998): 163-212. <http://eudml.org/doc/90518>.

@article{Asch1998,
author = {Asch, M., Lebeau, G.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
language = {eng},
pages = {163-212},
publisher = {EDP Sciences},
title = {Geometrical aspects of exact boundary controllability for the wave equation. A numerical study},
url = {http://eudml.org/doc/90518},
volume = {3},
year = {1998},
}

TY - JOUR
AU - Asch, M.
AU - Lebeau, G.
TI - Geometrical aspects of exact boundary controllability for the wave equation. A numerical study
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1998
PB - EDP Sciences
VL - 3
SP - 163
EP - 212
LA - eng
UR - http://eudml.org/doc/90518
ER -

References

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  1. [1] B. Allibert: Contrôle analytique de l'équation des ondes sur des surfaces de révolution, PhD thesis, École Polytechnique, 1997. 
  2. [2] M. Asch: Control and stabilization of wave propagation problems on complex geometries, in preparation, 1998. 
  3. [3] M. Asch, B. Vai: Une étude numérique du contrôle exacte du système de l'élasticité linéaire en dimension deux, Technical report 98-05, Laboratoire de Mathématiques, Université Paris-Sud, 1998. 
  4. [4] C. Bardos, G. Lebeau, J. Rauch: Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM Journal of Control and Optimization, 30, 1992, 1024-1065. Zbl0786.93009MR1178650
  5. [5] I. Charpentier, Y. Maday: Idetifications numériques de contrôles distribués pour l'équation des ondes, C. R. Acad. Sci. Paris Série I, 322, 1996, 779-784. Zbl0847.65043MR1387438
  6. [6] R. Glowinski: Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation, Journal of Computational Physics, 103, 1992, 189-221. Zbl0763.76042MR1196839
  7. [7] R. Glowinski, C.-H. Li, J.-L. Lions: A numerical approach to the exact controllability of the wave equation (I) Dirichlet controls: description of the numerical methods, Japan Journal of Applied Mathematics, 7, 1990, 1-76. Zbl0699.65055MR1039237
  8. [8] J.-L. Lions: Controlabilité exacte, perturbations et stabilisation de systèmes distribués, Tome I, Collection RMA, Masson, 1988. Zbl0653.93003
  9. [9] S. Micu, E. Zuazua: Boundary controllability of a linear hybrid System arising in the control of noise, SIAM Journal of Control and Optimization, 35, 1997, 1614-1637. Zbl0888.35017MR1466919
  10. [10] W.E. Milne: Numerical solution of differential equations, Dover Publications Inc., 1954. Zbl0228.65052MR347088

Citations in EuDML Documents

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  1. Sergei Ivanov, Control norms for large control times
  2. Sergei Ivanov, Control Norms for Large Control Times
  3. Arnaud Münch, A uniformly controllable and implicit scheme for the 1-D wave equation
  4. Arnaud Münch, A uniformly controllable and implicit scheme for the 1-D wave equation
  5. Mark Asch, Marion Darbas, Jean-Baptiste Duval, Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume
  6. Mark Asch, Marion Darbas, Jean-Baptiste Duval, Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

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