Exact controllability in short time for the wave equation

V. Komornik

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: 6, Issue: 2, page 153-164
  • ISSN: 0294-1449

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Komornik, V.. "Exact controllability in short time for the wave equation." Annales de l'I.H.P. Analyse non linéaire 6.2 (1989): 153-164. <http://eudml.org/doc/78171>.

@article{Komornik1989,
author = {Komornik, V.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {exact controllability; wave equation},
language = {eng},
number = {2},
pages = {153-164},
publisher = {Gauthier-Villars},
title = {Exact controllability in short time for the wave equation},
url = {http://eudml.org/doc/78171},
volume = {6},
year = {1989},
}

TY - JOUR
AU - Komornik, V.
TI - Exact controllability in short time for the wave equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - 6
IS - 2
SP - 153
EP - 164
LA - eng
KW - exact controllability; wave equation
UR - http://eudml.org/doc/78171
ER -

References

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  3. [FATTORINI] H. Fattorini, Estimates for Sequences Biorthogonal to Certain Complex Exponentials and Boundary Control of the Wave Equation, in Lecture Notes in Control and Information Science2, Springer-Verlag, Berlin, 1977. Zbl0379.93030MR490213
  4. [GRAHAM-RUSSELL] K.D. Graham and D.L. Russell, Boundary Control of the Wave Equation in a Spherical Region, SIAM J. Control, Vol. 13, 1975, pp. 174-196. Zbl0315.93004MR355756
  5. [GRISVARD] P. Grisvard, Contrôlabilité exacte des solutions de l'equation des ondes en présence de singularités, to appear. Zbl0683.49012
  6. [HARAUX 1] A. Haraux, Contrôlabilité exacte d'une membrane rectangulaire au moyen d'une fonctionnelle analytique localisée. C.R. Acad. Sci. Paris, série I Math., Vol. 306, 1988, pp. 125-128. Zbl0643.49029MR929104
  7. [HARAUX 2] A. Haraux, On a Completion Problem in the Theory of Distributed Control of Wave Equations, to appear. Zbl0731.93056
  8. [HO] L.F. Ho, Observabilité frontière de l'équation des ondes. C.R. Acad. Sci. Paris, série I Math., Vol. 302, 1986, pp. 443-446. Zbl0598.35060MR838598
  9. [KOMORNIK] V. Komornik, Contrôlabilité exacte en un temps minimal, C.R. Acad. Sci. Paris, série I Math., Vol. 304, 1987, pp. 223-225. Zbl0611.49027MR883479
  10. [KOMORNIK-ZUAZUA] V. Komornik and E. Zuazua, Stabilization frontière de l'équation des ondes : Une méthode directe, C.R. Acad. Sci. Paris, série I Math., Vol. 305, 1987, pp. 605-608. Zbl0661.93054MR917578
  11. [LAGNESE 1] J. Lagnese, Control of Wave Process with Distributed Controls Supported on a Subregion, SIAM J. Control and Opt., Vol. 21, No. 1, 1983, pp. 68-85. Zbl0512.93014MR688440
  12. [LAGNESE 2] J. Lagnese, Decay of Solutions of Wave Equations in a Bounded Region with Boundary Dissipation, J. Diff. Equations, Vol. 50, 1983, pp. 163-182. Zbl0536.35043MR719445
  13. [LASIECKA-TRIGGIANI] I. Lasiecka and R. Triggiani, Uniform Exponential Decay in a Bounded Region with L2 (0, T; L2 (Ω))-Feedback Control in the Dirichlet Boundary Conditions. J. Diff. Equations, Vol. 66, 1987, pp. 340-390. Zbl0629.93047MR876804
  14. [LIONS 1] J.L. Lions, Contrôle optimal des systèmes distribués singuliers, Dunod, Paris. 1983. Zbl0514.93001
  15. [LIONS 2] J.L. Lions, Contrôlabilité exact des systèmes distribués, C.R. Acad. Sci. Paris. série I Math., Vol. 302, 1986, pp. 471-475. Zbl0589.49022MR838402
  16. [LIONS 3] J.L. Lions, The John von Neumann Lecture, SIAM National Meeting, Boston, U.S.A., 1986. Zbl0606.49018
  17. [LIONS 4] J.L. Lions, Contrôlabilité exacte des systèmes distribués, Vol. 1-2, Masson. Collection R.M.A., 1988. Zbl0653.93003MR953547
  18. [LIONS-MAGENES] J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Paris, Dunod, 1968. Zbl0165.10801
  19. [RUSSELL] D.L. Russell, Controllability and Stabilizability Theory for Linear Partial Differential Equations. Recent Progress and Open Questions, SIAM Rev., Vol. 20, 1978. pp. 639-739. Zbl0397.93001MR508380
  20. [ZUAZUA] E. Zuazua, Contrôlabilité exacte d'un modèle de plaques vibrantes en un temps arbitrairement petit, C.R. Acad. Sci. Paris, série I Math., Vol. 304, 1986, pp. 173-176. Zbl0611.49028

Citations in EuDML Documents

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  1. Vilmos Komornik, A new method of exact controllability in short time and applications
  2. Weijiu Liu, Graham Williams, Exact Neumann boundary controllability for second order hyperbolic equations
  3. M. M. Cavalcanti, Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients
  4. Aissa Guesmia, On the nonlinear stabilization of the wave equation
  5. Marcelo Moreira Cavalcanti, Exact controllability of the wave equation with Neumann boundary condition and time-dependent coefficients
  6. Patrick Martinez, A new method to obtain decay rate estimates for dissipative systems

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