Free Access
Issue
ESAIM: COCV
Volume 13, Number 3, July-September 2007
Page(s) 503 - 527
DOI https://doi.org/10.1051/cocv:2007020
Published online 05 June 2007
  1. H.T. Banks and K. Kunisch, The linear regulator problem for parabolic systems. SIAM J. Control Optim. 22 (1984) 684–698. [CrossRef] [MathSciNet] [Google Scholar]
  2. H.T. Banks, K. Ito and C. Wang, Exponentially stable approximations of weakly damped wave equations, in Estimation and control of distributed parameter systems (Vorau, 1990), Birkhäuser, Basel, Internat. Ser. Numer. Math. 100 (1991) 1–33. [Google Scholar]
  3. G. Chen, S.A. Fulling, F.J. Narcowich and S. Sun, Exponential decay of energy of evolution equations with locally distributed damping. SIAM J. Appl. Math. 51 (1991) 266–301. [CrossRef] [MathSciNet] [Google Scholar]
  4. R.F. Curtain and H. Zwart, An introduction to infinite-dimensional linear systems theory, Texts in Applied Mathematics 21. Springer-Verlag, New York (1995). [Google Scholar]
  5. E. Fernandez-Cara and E. Zuazua, On the null controllability of the one-dimensional heat equation with BV coefficients. Comput. Appl. Math. 21 (2002) 167–190. [MathSciNet] [Google Scholar]
  6. J.S. Gibson, An analysis of optimal modal regulation: convergence and stability. SIAM J. Control Optim. 19 (1981) 686–707. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.S. Gibson and A. Adamian, Approximation theory for linear-quadratic-Gaussian optimal control of flexible structures. SIAM J. Control Optim. 29 (1991) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  8. R. Glowinski, C.H. Li and J.-L. Lions, A numerical approach to the exact boundary controllability of the wave equation. I. Dirichlet controls: description of the numerical methods. Japan J. Appl. Math. 7 (1990) 1–76. [CrossRef] [MathSciNet] [Google Scholar]
  9. F.L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces. Ann. Differ. Equ. 1 (1985) 43–56. [Google Scholar]
  10. J.A. Infante and E. Zuazua, Boundary observability for the space semi-discretizations of the 1-D wave equation. ESAIM: M2AN 33 (1999) 407–438. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  11. F. Kappel and D. Salamon, An approximation theorem for the algebraic Riccati equation. SIAM J. Control Optim. 28 (1990) 1136–1147. [CrossRef] [MathSciNet] [Google Scholar]
  12. Z. Liu and S. Zheng, Semigroups associated with dissipative systems, Notes in Mathematics 398. Chapman & Hall/CRC Research, Chapman (1999). [Google Scholar]
  13. M. Naimark, Linear differential operators. Ungar, New York (1967). [Google Scholar]
  14. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, Appl. Math. Sci. 44 (1983). [Google Scholar]
  15. J. Prüss, On the spectrum of Formula -semigroups. Trans. Amer. Math. Soc. 284 (1984) 847–857. [CrossRef] [MathSciNet] [Google Scholar]
  16. P.-A. Raviart and J.-M. Thomas, Introduction à l'analyse numérique des équations aux dérivées partielles. Dunod, Paris (1998). [Google Scholar]
  17. G. Strang and G.J. Fix, An analysis of the finite element method. Prentice-Hall Inc., Englewood Cliffs, N.J. Prentice-Hall Series in Automatic Computation (1973). [Google Scholar]
  18. L.R. Tcheugoué Tébou and E. Zuazua, Uniform exponential long time decay for the space semi-discretization of a locally damped wave equation via an artificial numerical viscosity. Numer. Math. 95 (2003) 563–598. [CrossRef] [MathSciNet] [Google Scholar]
  19. E. Zuazua, Boundary observability for the finite-difference space semi-discretizations of the 2-D wave equation in the square. J. Math. Pures Appl. 78 (1999) 523–563. [CrossRef] [MathSciNet] [Google Scholar]
  20. E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet] [Google Scholar]

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