@article{M2AN_1999__33_2_407_0, author = {Infante, Juan Antonio and Zuazua, Enrique}, title = {Boundary observability for the space semi-discretizations of the $1-d$ wave equation}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {407--438}, publisher = {EDP-Sciences}, volume = {33}, number = {2}, year = {1999}, mrnumber = {1700042}, zbl = {0947.65101}, language = {en}, url = {http://www.numdam.org/item/M2AN_1999__33_2_407_0/} }
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: Modélisation mathématique et analyse numérique PY - 1999 SP - 407 EP - 438 VL - 33 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_1999__33_2_407_0/ LA - en ID - M2AN_1999__33_2_407_0 ER -
%0 Journal Article %A Infante, Juan Antonio %A Zuazua, Enrique %T Boundary observability for the space semi-discretizations of the $1-d$ wave equation %J ESAIM: Modélisation mathématique et analyse numérique %D 1999 %P 407-438 %V 33 %N 2 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_1999__33_2_407_0/ %G en %F M2AN_1999__33_2_407_0
Infante, Juan Antonio; Zuazua, Enrique. Boundary observability for the space semi-discretizations of the $1-d$ wave equation. ESAIM: Modélisation mathématique et analyse numérique, Volume 33 (1999) no. 2, pp. 407-438. http://www.numdam.org/item/M2AN_1999__33_2_407_0/
[1] Contrôlabilité exacte, homogénéisation et localisation d'ondes dans un milieu non-homogène. Asymptotic Analysis 5 (1992) 481-494. | MR | Zbl
, and ,[2] Contrôle de l'équation des ondes à densité rapidement oscillante à une dimension d'espace. C. R. Acad. Sci. Paris 324 (1997) 1237-1242. | MR | Zbl
and ,[3] Ensuring Weli-Posedness by Analogy; Stokes Problem and Boundary Control for the Wave Equation. J. Comput.Phys. 103 (1992) 189-221. | MR | Zbl
,[4] A numerical approach to the exact boundary controllability of the wave equation. (I).Dirichlet Controls: Description of the numerical methods. Jap. J. Appl. Math. 7 (1990) 1-76. | MR | Zbl
, and ,[5] Exact and approximate controllability for distributed parameter Systems. Acta Numerica (1996)159-333. | MR | Zbl
and ,[6] Boundary observability for the space-discretizations of the 1 - d wave equation. C. R. Acad. Sci.Paris 326 (1998) 713-718. | MR | Zbl
and ,[7] Some trigonometrical inequalities with applications to the theory of series. Mathematische Zeitschrift 41 (1936) 367-379. | MR | Zbl
,[8] Analysis of Numerical Methods. John Wiley & Sons (1966). | MR | Zbl
and ,[9] Exact controllability and stabilization. The multiplier method. John Wiley & Sons, Masson (1994). | MR | Zbl
,[10] Foundations of Optimal Control Theory, The SIAM Series in Applied Mathematics. John Wiley & Sons (1967). | MR | Zbl
and ,[11] Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. Tome 1. Contrôlabilité exacte. Masson,RMA8 (1988). | Zbl
,[12] Fourier analysis of numerical approximations of hyperbolic equations. SIAM, Philadelphia(1982). | MR | Zbl
and ,