Free access
Issue
ESAIM: COCV
Volume 13, Number 3, July-September 2007
Page(s) 503 - 527
DOI http://dx.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]
  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.
  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]
  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).
  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]
  6. J.S. Gibson, An analysis of optimal modal regulation: convergence and stability. SIAM J. Control Optim. 19 (1981) 686–707. [CrossRef] [MathSciNet]
  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]
  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]
  9. F.L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces. Ann. Differ. Equ. 1 (1985) 43–56.
  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]
  11. F. Kappel and D. Salamon, An approximation theorem for the algebraic Riccati equation. SIAM J. Control Optim. 28 (1990) 1136–1147. [CrossRef] [MathSciNet]
  12. Z. Liu and S. Zheng, Semigroups associated with dissipative systems, Notes in Mathematics 398. Chapman & Hall/CRC Research, Chapman (1999).
  13. M. Naimark, Linear differential operators. Ungar, New York (1967).
  14. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, Appl. Math. Sci. 44 (1983).
  15. J. Prüss, On the spectrum of Formula -semigroups. Trans. Amer. Math. Soc. 284 (1984) 847–857. [CrossRef] [MathSciNet]
  16. P.-A. Raviart and J.-M. Thomas, Introduction à l'analyse numérique des équations aux dérivées partielles. Dunod, Paris (1998).
  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).
  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]
  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]
  20. E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet]