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All issues Volume 13 / No 2 (April-June 2007) ESAIM: COCV, 13 2 (2007) 265-293 References
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Issue
ESAIM: COCV
Volume 13, Number 2, April-June 2007
Page(s) 265 - 293
DOI https://doi.org/10.1051/cocv:2007009
Published online 12 May 2007
  1. M. Asch and G. Lebeau, The spectrum of the damped wave operator for geometrically complex domain in Formula . Experimental Math. 12 (2003) 227–241. [Google Scholar]
  2. H.T. Banks, K. Ito and B. Wang, Exponentially stable approximations of weakly damped wave equations. Ser. Num. Math. 100 Birkhäuser (1990) 1–33. [Google Scholar]
  3. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization from the boundary. SIAM J. Control Opt. 30 (1992) 1024–1065. [CrossRef] [Google Scholar]
  4. D. Chenais, On the existence of a solution in a domain identification problem. J. Math. Anal. Appl. 52 (1975) 189–219. [CrossRef] [MathSciNet] [Google Scholar]
  5. G.C. Cohen, Higher-order Numerical Methods for Transient Wave Equations. Scientific Computation, Springer (2002). [Google Scholar]
  6. C.M. Dafermos, On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity. Arch. Rational Mech. Anal. 29 (1968) 241–271. [Google Scholar]
  7. 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]
  8. A. Haraux, Stabilization of trajectories for some weakly damped hyperbolic equations. J. Differential Equations 59 (1985) 145–154. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Haraux, Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps. Portug. Math. 46 (1989) 245–258. [Google Scholar]
  10. A. Henrot, Continuity with respect to the domain for the Laplacian: a survey. Control Cybernetics 23 (1994) 427–443. [Google Scholar]
  11. J.A. Infante and E. Zuazua, Boundary observability for the space-discretizations of the 1-D wave equation. ESAIM: M2AN 33 (1999) 407–438. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  12. V. Komornik, Exact Controllability and Stabilization - The Multiplier Method. J. Wiley and Masson (1994). [Google Scholar]
  13. S. Krenk, Dispersion-corrected explicit integration of the wave equation. Comput. Methods Appl. Mech. Engrg. 191 (2001) 975–987. [Google Scholar]
  14. J. Lagnese, Control of wave processes with distributed control supported on a subregion. SIAM J. Control Opt. 21 (1983) 68–85. [CrossRef] [Google Scholar]
  15. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod-Gauthier-Villars, Paris (1969). [Google Scholar]
  16. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris (1968). [Google Scholar]
  17. A. Münch, A uniformly controllable and implicit scheme for the 1-D wave equation. ESAIM: M2AN 39 (2005) 377–418. [CrossRef] [EDP Sciences] [Google Scholar]
  18. M. Nakao, Decay of solutions of the wave equation with a local degenerate dissipation. Israel J. Math. 95 (1996) 25–42. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Negreanu and E. Zuazua, Discrete Ingham inequalities and applications. C.R. Acad. Sci. Paris 338 (2004) 281–286. [Google Scholar]
  20. O. Pironneau, Optimal shape design for elliptic systems. New York, Springer (1984). [Google Scholar]
  21. K. Ramdani, T. Takahashi and M. Tucsnak, Uniformly exponentially stable approximations for a class of second order evolution equations: Application to the optimal controle of flexible structures. Technical report, Prépublications de l'Institut Elie Cartan 27 (2003). [Google Scholar]
  22. M. Slemrod, Weak asymptotic decay via a “Relaxed Invariance Principle” for a wave equation with nonlinear, nonmonotone damping. Proc. Royal Soc. Edinburgh 113 (1989) 87–97. [Google Scholar]
  23. L.R. Tcheugoué-Tébou, Stabilization of the wave equation with localized nonlinear damping. J. Differential Equations 145 (1998) 502–524. [Google Scholar]
  24. 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. [Google Scholar]
  25. E. Zuazua, Exponential decay for the semilinear wave equation with locally distributed damping. Comm. Partial Differential Equation 15 (1990) 205–235. [Google Scholar]
  26. E. Zuazua, Boundary observability for finite-difference space semi-discretizations of the 2-D wave equation in the square. J. Math. Pures Appl. 78 (1999) 523–563. [Google Scholar]
  27. E. Zuazua, Optimal and approximate control of finite-difference approximation schemes for the 1-D wave equation. Rendiconti di Matematica, Serie VIII 24 (2004) 201–237. [Google Scholar]
  28. E. Zuazua, Propagation, observation, control and numerical approximation of waves. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet] [Google Scholar]

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