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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 33 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 33
Number of page(s) 27
DOI https://doi.org/10.1051/cocv/2024025
Published online 16 April 2024
  1. 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]
  2. R. Glowinski and J.-L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numer. 5 (1996) 159–333. [Google Scholar]
  3. R. Glowinski, J.-L. Lions and J. He, Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach, Encyclopedia of Mathematics and its Applications, Vol. 117. Cambridge University Press, New York (2008). [Google Scholar]
  4. S. Ervedoza and E. Zuazua, On the numerical approximation of exact controls for waves. Springer Briefs in Mathematics. Springer, New York (2013). [CrossRef] [Google Scholar]
  5. E. Trélat and E. Zuazua, editors. Numerical Control: Part A, Vol. 23 of Handbook of Numerical Analysis. North Holland, Amsterdam (2022). [Google Scholar]
  6. E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Rosier and L. Rosier, Numerical control of the wave equation and Huygens’ principle. Math. Rep. 24 (2022) 319–338. [Google Scholar]
  8. B. Laroche, P. Martin and P. Rouchon, Motion planning for the heat equation. Int. J. Robust Nonlinear Control 10 (2000) 629–643. [CrossRef] [Google Scholar]
  9. P. Martin, L. Rosier and P. Rouchon, Null controllability of the heat equation using flatness. Automatica 50 (2014) 3067–3076. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. Russell, Exact boundary value controllability theorems for wave and heat processes in star-complemented regions, in Differential Games and Control Theory (Proc. NSF-CBMS Regional Res. Conf. University of Rhode Island, Kingston, RI (1973). Lecture Notes Pure Appl. Math. 10 (1974) 291–319. Dekker, New York. [Google Scholar]
  11. G. Chen, Control and stabilization for the wave equation in a bounded domain. SIAM J. Control Optim. 17 (1979) 66–81. [Google Scholar]
  12. R. Rebarber and G. Weiss, An extension of Russell’s principle on exact controllability, in Proceedings of the Fourth ECC, 1997. CD-ROM. [Google Scholar]
  13. K. Ramdani, M. Tucsnak and G. Weiss, Recovering the initial state of an infinite-dimensional system using observers. Automatica 46 (2010) 1616–1625. [CrossRef] [MathSciNet] [Google Scholar]
  14. S.W. Hansen and M. Tucsnak, Some new applications of Russell’s principle to infinite dimensional vibrating systems. Annu. Rev. Control 44 (2017) 184–198. [CrossRef] [Google Scholar]
  15. M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups. Birkhäuser Advanced Texts, Springer, Basel (2009). [CrossRef] [Google Scholar]
  16. P. Pedregal, F. Periago and J. Villena, A numerical method of local energy decay for the boundary controllability of time-reversible distributed parameter systems. Stud. Appl. Math. 121 (2008) 27–47. [CrossRef] [MathSciNet] [Google Scholar]
  17. N. Cindea, S. Micu and M. Tucsnak, An approximation method for exact controls of vibrating systems. SIAM J. Control Optim. 49 (2011) 1283–1305. [CrossRef] [MathSciNet] [Google Scholar]
  18. H.T. Banks, K. Ito and B. Wang, Exponentially stable approximations of weakly damped wave equations, in International Series of Numerical Mathematics, Vol. 100. Birkhäuser, Basel (1991) 1–33. [CrossRef] [Google Scholar]
  19. U. Biccari, A. Marica and E. Zuazua, Propagation of one- and two-dimensional discrete waves under finite difference approximation, Found. Comput. Math. 20 (2020) 1401–1438. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Ervedoza, Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes. Numer. Math. 113 (2009) 377–415. [Google Scholar]
  21. S. Ervedoza and E. Zuazua, Uniformly exponentially stable approximations for a class of damped systems. J. Math. Pures Appl. 91 (2009) 20–48. [Google Scholar]
  22. S. Ervedoza and E. Zuazua, The Wave Equation: Control and Numerics. Control and Stabilization of PDEs, edited by P.M. Cannarsa and J.M. Coron. Lecture Notes Math. 2048 (2012) 245–340. [CrossRef] [Google Scholar]
  23. A. Münch and A.F. Pazoto, Uniform stabilization of a viscous numerical approximation for a locally damped wave equation. ESAIM: COCV 13 (2007) 265–293. [CrossRef] [EDP Sciences] [Google Scholar]
  24. K. Ramdani, T. Takahashi and M. Tucsnak, Uniformly exponentially stable approximations for a class of second order evolution equations. Application to LQR optimization problems. ESAIM: COCV 13 (2007) 503–527. [CrossRef] [EDP Sciences] [Google Scholar]
  25. L.R. Tcheugoue Tebou 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]
  26. L.T. Tebou and E. Zuazua, Uniform boundary stabilization of the finite difference space discretization of the 1-D wave equation. Adv. Comput. Math. 26 (2007) 337–365. [CrossRef] [MathSciNet] [Google Scholar]
  27. P.A. Raviart and J.M. Thomas, Introduction à l’analyse numérique des équations aux dérivées partielles. Masson (1998). [Google Scholar]
  28. N. Cîndea, S. Micu and J. Morais Pereira, Approximation of periodic solutions for a dissipative hyperbolic equation. Numer. Math. 124 (2013) 559–601. [Google Scholar]
  29. K. Ito, K. Ramdani and M. Tucsnak, A time reversal based algorithm for solving initial data inverse problems. AIMS 4 (2011) 641–652. [Google Scholar]
  30. K. Ramdani, T. Takahashi and M. Tucsnak, Space semidiscretization of the problem of internal stabilization for the beam equation. ESAIM: Proc. 18 (2007) 48–56. [CrossRef] [EDP Sciences] [Google Scholar]

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