Uniformly Controllable Schemes for the Wave Equation on the Unit Square, Journal of Optimization Theory and Applications, vol.20, issue.3, pp.417-438, 2009. ,
DOI : 10.1007/s10957-009-9569-5
URL : https://hal.archives-ouvertes.fr/hal-00482826
Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary, SIAM Journal on Control and Optimization, vol.30, issue.5, pp.1024-1065, 1992. ,
DOI : 10.1137/0330055
Lipschitz stability in an inverse problem for the wave equation, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00598876
Global Carleman Estimates for Waves and Applications, Communications in Partial Differential Equations, vol.75, issue.5 ,
DOI : 10.1137/S0363012999350298
URL : https://hal.archives-ouvertes.fr/hal-00633562
Convergence of an Inverse Problem for a 1-D Discrete Wave Equation, SIAM Journal on Control and Optimization, vol.51, issue.1 ,
DOI : 10.1137/110838042
Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square, IMA Journal of Numerical Analysis, vol.28, issue.1, pp.186-214, 2008. ,
DOI : 10.1093/imanum/drm012
URL : https://hal.archives-ouvertes.fr/hal-00484055
An approximation method for the exact controls of vibrating systems, SIAM. J. Control. Optim, vol.49, pp.1283-1305, 2011. ,
Analysis of the HUM Control Operator and Exact Controllability for Semilinear Waves in Uniform Time, SIAM Journal on Control and Optimization, vol.48, issue.2, pp.521-550, 2009. ,
DOI : 10.1137/070712067
Experimental Study of the HUM Control Operator for Linear Waves, Experimental Mathematics, vol.19, issue.1, pp.93-120, 2010. ,
DOI : 10.1080/10586458.2010.10129063
URL : https://hal.archives-ouvertes.fr/inria-00418712
Convex analysis and variational problems, Classics in Applied Mathematics Society for Industrial and Applied Mathematics (SIAM), vol.28, 1999. ,
DOI : 10.1137/1.9781611971088
The Wave Equation: Control and Numerics, Control of partial differential equations, Lecture notes in mathematics, CIME Subseries, 2011. ,
DOI : 10.1007/978-3-642-27893-8_5
URL : https://hal.archives-ouvertes.fr/hal-00991988
Strong convergent approximations of null controls for the 1D heat equation, SeMA Journal, vol.III, issue.8, 2013. ,
DOI : 10.1007/s40324-013-0001-6
Numerical null controllability of the 1-d heat equation: Carleman weights and duality, Preprint, 2010. ,
Numerical null controllability of a semi-linear 1D heat via a least squares reformulation, C.R. Acad. Sci. Série I, vol.349, pp.867-871, 2011. ,
Numerical null controllability of semi-linear 1D heat equations: fixed points, least squares and Newton methods, Mathematical Control and Related Fields, vol.2, issue.3, pp.217-246, 2012. ,
Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series, number 34, pp.1-163, 1996. ,
Exact Controllability for Multidimensional Semilinear Hyperbolic Equations, SIAM Journal on Control and Optimization, vol.46, issue.5, pp.1578-1614, 2007. ,
DOI : 10.1137/040610222
Imanuvilov, On Carleman estimates for hyperbolic equations, Asymptotic Analysis, pp.185-220, 2002. ,
Exact and approximate controllability for distributed parameter systems, Acta Numerica, pp.159-333, 1996. ,
On the controllability of wave models with variable coefficients: a numerical investigation, Computational and Applied Mathematics, vol.21, issue.1, pp.191-225, 2002. ,
Exact and approximate controllability for distributed parameter systems: a numerical approach Encyclopedia of Mathematics and its Applications, 2008. ,
Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems, Applied Mathematics & Optimization, vol.137, issue.1, pp.109-154, 1991. ,
DOI : 10.1007/BF01442394
A uniformly controllable and implicit scheme for the 1-D wave equation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.2, pp.377-418, 2005. ,
DOI : 10.1051/m2an:2005012
Optimal design of the support of the control for the 2-D wave equation: a numerical method, Int. J. Numer. Anal. Model, vol.5, pp.331-351, 2008. ,
Optimal shape and position of the support for the internal exact control of a string, Systems & Control Letters, vol.58, issue.2, pp.136-140, 2009. ,
DOI : 10.1016/j.sysconle.2008.08.007
Convex Functions and Duality in Optimization Problems and Dynamics, Lecture Notes Oper. Res. and Math. Ec, vol.II, 1969. ,
DOI : 10.1007/978-3-642-46196-5_7
A Unified Boundary Controllability Theory for Hyperbolic and Parabolic Partial Differential Equations, Studies in Applied Mathematics, vol.40, issue.3, pp.189-221, 1973. ,
DOI : 10.1002/sapm1973523189
Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions, SIAM Rev, pp.639-739, 1978. ,
Carleman estimates and unique continuation for solutions to boundary value problems, J. Math. Pures Appl, vol.75, pp.367-408, 1996. ,
On The Observability Inequalities for Exact Controllability of Wave Equations With Variable Coefficients, SIAM Journal on Control and Optimization, vol.37, issue.5, pp.1568-1599, 1999. ,
DOI : 10.1137/S0363012997331482
Explicit Observability Inequalities for the Wave Equation with Lower Order Terms by Means of Carleman Inequalities, SIAM Journal on Control and Optimization, vol.39, issue.3, pp.812-834, 2000. ,
DOI : 10.1137/S0363012999350298
Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods, SIAM Review, vol.47, issue.2, pp.197-243, 2005. ,
DOI : 10.1137/S0036144503432862
Control and numerical approximation of the wave and heat equations, International Congress of Mathematicians, pp.1389-1417, 2006. ,
DOI : 10.4171/022-3/67