Boundary observability for the space semi-discretizations of the 1 - d wave equation

Juan Antonio Infante; Enrique Zuazua

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 2, page 407-438
  • ISSN: 0764-583X

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Infante, Juan Antonio, and Zuazua, Enrique. "Boundary observability for the space semi-discretizations of the $1-d$ wave equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.2 (1999): 407-438. <http://eudml.org/doc/193927>.

@article{Infante1999,
author = {Infante, Juan Antonio, Zuazua, Enrique},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {wave equation; semi-discretization; finite difference; finite element; boundary observability},
language = {eng},
number = {2},
pages = {407-438},
publisher = {Dunod},
title = {Boundary observability for the space semi-discretizations of the $1-d$ wave equation},
url = {http://eudml.org/doc/193927},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Infante, Juan Antonio
AU - Zuazua, Enrique
TI - Boundary observability for the space semi-discretizations of the $1-d$ wave equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 2
SP - 407
EP - 438
LA - eng
KW - wave equation; semi-discretization; finite difference; finite element; boundary observability
UR - http://eudml.org/doc/193927
ER -

References

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  2. [2] C. Castro and E. Zuazua, Contrôle de l'équation des ondes à densité rapidement oscillante à une dimension d'espace. C. R. Acad. Sci. Paris 324 (1997) 1237-1242. Zbl1007.93036MR1456294
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  5. [5] R. Glowinski and J. L. Lions, Exact and approximate controllability for distributed parameter Systems. Acta Numerica (1996)159-333. Zbl0838.93014MR1352473
  6. [6] J. A. Infante and E. Zuazua, Boundary observability for the space-discretizations of the 1 - d wave equation. C. R. Acad. Sci.Paris 326 (1998) 713-718. Zbl0910.65051MR1641762
  7. [7] A. E. Ingham, Some trigonometrical inequalities with applications to the theory of series. Mathematische Zeitschrift 41 (1936) 367-379. Zbl0014.21503MR1545625
  8. [8] E. Isaacson and H. B. Keller, Analysis of Numerical Methods. John Wiley & Sons (1966). Zbl0168.13101MR201039
  9. [9] V. Komornik, Exact controllability and stabilization. The multiplier method. John Wiley & Sons, Masson (1994). Zbl0937.93003MR1359765
  10. [10] E. B. Lee and L. Markus, Foundations of Optimal Control Theory, The SIAM Series in Applied Mathematics. John Wiley & Sons (1967). Zbl0159.13201MR220537
  11. [11] J. L. Lions, Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. Tome 1. Contrôlabilité exacte. Masson,RMA8 (1988). Zbl0653.93002
  12. [12] R. Vichnevetsky and J. B. Bowles, Fourier analysis of numerical approximations of hyperbolic equations. SIAM, Philadelphia(1982). Zbl0495.65041MR675265

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