Free Access
Volume 19, Number 4, October-December 2013
Page(s) 1076 - 1108
Published online 13 August 2013
  1. M. Asch and A. Münch, An implicit scheme uniformly controllable for the 2-D wave equation on the unit square. J. Optimiz. Theory Appl. 143 (2009) 417–438. [CrossRef] [MathSciNet] [Google Scholar]
  2. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Optim. 30 (1992) 1024–1065. [Google Scholar]
  3. L. Baudouin, Lipschitz stability in an inverse problem for the wave equation, Master report (2001) available at: [Google Scholar]
  4. L. Baudouin, M. de Buhan and S. Ervedoza, Global Carleman estimates for wave and applications. Preprint. [Google Scholar]
  5. L. Baudouin and S. Ervedoza, Convergence of an inverse problem for discrete wave equations. Preprint. [Google Scholar]
  6. C. Castro, S. Micu and A. Münch, Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square. IMA J. Numer. Anal. 28 (2008) 186–214. [CrossRef] [MathSciNet] [Google Scholar]
  7. N. Cîndea, S. Micu and M. Tucsnak, An approximation method for the exact controls of vibrating systems. SIAM. J. Control. Optim. 49 (2011) 1283–1305. [CrossRef] [MathSciNet] [Google Scholar]
  8. B. Dehman and G. Lebeau, Analysis of the HUM control operator and exact controllability for semilinear waves in uniform time. SIAM. J. Control. Optim. 48 (2009) 521–550. [Google Scholar]
  9. G. Lebeau and M. Nodet, Experimental study of the HUM control operator for linear waves. Experiment. Math. 19 (2010) 93–120. [CrossRef] [MathSciNet] [Google Scholar]
  10. I. Ekeland and R. Temam, Convex analysis and variational problems, Classics in Applied Mathematics. Soc. Industr. Appl. Math. SIAM, Philadelphia 28 (1999). [Google Scholar]
  11. S. Ervedoza and E. Zuazua, The wave equation: Control and numerics. In Control of partial differential equations of Lect. Notes Math. Edited by P.M. Cannarsa and J.M. Coron. CIME Subseries, Springer Verlag (2011). [Google Scholar]
  12. E. Fernández-Cara and A. Münch, Strong convergent approximations of null controls for the heat equation. Séma Journal 61 (2013) 49–78. [Google Scholar]
  13. E. Fernández-Cara and A. Münch, Numerical null controllability of the 1-d heat equation: Carleman weights and duality. Preprint (2010). Available at [Google Scholar]
  14. E. Fernández-Cara and A. Münch, Numerical null controllability of a semi-linear 1D heat via a least squares reformulation. C.R. Acad. Sci. Série I 349 (2011) 867–871. [CrossRef] [Google Scholar]
  15. E. Fernández-Cara and A. Münch, Numerical null controllability of semi-linear 1D heat equations: fixed points, least squares and Newton methods. Math. Control Related Fields 2 (2012) 217–246. [CrossRef] [Google Scholar]
  16. A.V. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations, in vol. 34 of Lecture Notes Series. Seoul National University, Korea (1996) 1–163. [Google Scholar]
  17. X. Fu, J. Yong, and X. Zhang, Exact controllability for multidimensional semilinear hyperbolic equations. SIAM J. Control Optim. 46 (2007) 1578–1614. [CrossRef] [MathSciNet] [Google Scholar]
  18. O. Yu. Imanuvilov, On Carleman estimates for hyperbolic equations. Asymptotic Analysis 32 (2002) 185–220. [Google Scholar]
  19. R. Glowinski and J.L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numerica (1996) 159–333. [Google Scholar]
  20. R. Glowinski, J. He and J.L. Lions, On the controllability of wave models with variable coefficients: a numerical investigation. Comput. Appl. Math. 21 (2002) 191–225. [MathSciNet] [Google Scholar]
  21. R. Glowinski, J. He and J.L. Lions, Exact and approximate controllability for distributed parameter systems: a numerical approach in vol. 117 of Encyclopedia Math. Appl. Cambridge University Press, Cambridge (2008). [Google Scholar]
  22. I. Lasiecka and R. Triggiani, Exact controllability of semi-linear abstract systems with applications to waves and plates boundary control. Appl. Math. Optim. 23 (1991) 109–154. [CrossRef] [MathSciNet] [Google Scholar]
  23. J-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Recherches en Mathématiques Appliquées, Tomes 1 et 2. Masson. Paris (1988). [Google Scholar]
  24. 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]
  25. A. Münch, Optimal design of the support of the control for the 2-D wave equation: a numerical method. Int. J. Numer. Anal. Model. 5 (2008) 331–351. [Google Scholar]
  26. P. Pedregal, A variational perspective on controllability. Inverse Problems 26 (2010) 015004. [CrossRef] [MathSciNet] [Google Scholar]
  27. F. Periago, Optimal shape and position of the support of the internal exact control of a string. Systems Control Lett. 58 (2009) 136–140. [CrossRef] [MathSciNet] [Google Scholar]
  28. E.T. Rockafellar, Convex functions and duality in optimization problems and dynamics. In vol. II of Lect. Notes Oper. Res. Math. Ec. Springer, Berlin (1969). [Google Scholar]
  29. D.L. Russell, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Studies Appl. Math. 52 (1973) 189–221. [Google Scholar]
  30. D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions. SIAM Rev. 20 (1978) 639–739. [CrossRef] [MathSciNet] [Google Scholar]
  31. D. Tataru, Carleman estimates and unique continuation for solutions to boundary value problems. J. Math. Pures Appl. 75 (1996) 367–408. [Google Scholar]
  32. P-F. Yao, On the observability inequalities for exact controllability of wave equations with variable coefficients. SIAM J. Control. Optim. 37 (1999) 1568–1599. [CrossRef] [MathSciNet] [Google Scholar]
  33. X. Zhang, Explicit observability inequalities for the wave equation with lower order terms by means of Carleman inequalities. SIAM J. Control. Optim. 39 (2000) 812–834. [Google Scholar]
  34. E. Zuazua, Propagation, observation, control and numerical approximations of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet] [Google Scholar]
  35. E. Zuazua, Control and numerical approximation of the wave and heat equations. In vol. III of Intern. Congress Math. Madrid, Spain (2006) 1389–1417. [Google Scholar]

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