A. Alla and M. Falcone, An adaptive POD approximation method for the control of advectiondiffusion equations, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00800433

A. Altarovici, O. Bokanowski, and H. Zidani, A general Hamilton-Jacobi framework for nonlinear state constrained control problems, ESAIM Control Optim. Calc. Var, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00653337

H. T. Banks and K. Kunisch, The Linear Regulator Problem for Parabolic Systems, SIAM Journal on Control and Optimization, vol.22, issue.5, pp.499-515, 1984.
DOI : 10.1137/0322043

E. Bänsch and P. Benner, Stabilization of incompressible flow problems by Riccati-based feedback , Constrained Optimization and Optimal Control for Partial Differential Equations, Birkhäuser

V. Barbu, S. S. Rodrigues, and A. Shirikyan, Internal Exponential Stabilization to a Nonstationary Solution for 3D Navier???Stokes Equations, SIAM Journal on Control and Optimization, vol.49, issue.4, pp.1454-1478, 2011.
DOI : 10.1137/100785739

URL : https://hal.archives-ouvertes.fr/hal-00455250

M. Bardi and I. Capuzzo-dolcetta, Optimal Control and Viscosity Solutions of Hamilton- Jacobi-Bellman Equations, 2008.
DOI : 10.1007/978-0-8176-4755-1

O. Bokanowski, Y. Cheng, and C. Shu, A discontinuous Galerkin scheme for front propagation with obstacles, Numerische Mathematik, vol.48, issue.6, 2013.
DOI : 10.1007/s00211-013-0555-3

URL : https://hal.archives-ouvertes.fr/hal-00653532

O. Bokanowski, E. Cristiani, and H. Zidani, An Efficient Data Structure and Accurate Scheme to??Solve Front Propagation Problems, Journal of Scientific Computing, vol.114, issue.2, pp.251-273, 2010.
DOI : 10.1007/s10915-009-9329-6

O. Bokanowski, A. Desilles, H. Zidani, and R. , A C++ library for solving HJ equations, 2013.

O. Bokanowski, N. Forcadel, and H. Zidani, Reachability and Minimal Times for State Constrained Nonlinear Problems without Any Controllability Assumption, SIAM Journal on Control and Optimization, vol.48, issue.7, pp.4292-4316, 2010.
DOI : 10.1137/090762075

URL : https://hal.archives-ouvertes.fr/hal-00395589

O. Bokanowski, J. Garcke, M. Griebel, and I. Klompmaker, An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations, Journal of Scientific Computing, vol.24, issue.7, pp.575-605, 2012.
DOI : 10.1007/s10915-012-9648-x

URL : https://hal.archives-ouvertes.fr/hal-00741178

O. Bokanowski, N. Megdich, and H. Zidani, Convergence of a non-monotone scheme for Hamilton???Jacobi???Bellman equations with discontinous initial data, Numerische Mathematik, vol.29, issue.4, pp.1-44, 2010.
DOI : 10.1007/s00211-009-0271-1

J. Buchot, L. Thevenet, and J. P. Raymond, Nonlinear feedback stabilization of a two dimensional Burgers equation, ESAIM Control Optim. Calc. Var, vol.16, pp.929-955, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00629863

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods, 2007.
DOI : 10.1002/0470091355.ecm003m

URL : https://hal.archives-ouvertes.fr/hal-01296839

M. Falcone and R. Ferreti, Semi-Lagrangian Approximation Schemes for Linear and Hamilton- Jacobi Equations
DOI : 10.1137/1.9781611973051

URL : https://hal.archives-ouvertes.fr/hal-00916055

R. Ferretti, Internal approximation schemes for optimal control problems in Hilbert spaces, 1997.

L. Gaudio and A. Quarteroni, Spectral Element Discretization of Optimal Control Problems, Lecture Notes in Computational Science and Engineering, vol.76, pp.393-401, 2011.
DOI : 10.1007/978-3-642-15337-2_37

M. Gerdts, G. Greif, and H. J. Pesch, Numerical optimal control of the wave equation: optimal boundary control of a string to rest in finite time, Mathematics and Computers in Simulation, vol.79, issue.4, pp.1020-1032, 2008.
DOI : 10.1016/j.matcom.2008.02.014

J. S. Gibson, An analysis of optimal modal regulation: convergence and stability A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems, SIAM J. Cont. Optim. SIAM J. Cont. Optim, vol.1920, issue.5 3, pp.686-707, 1981.

S. Gombao and J. Raymond, Hamilton-Jacobi equations for control problems of parabolic equations, ESAIM: Control, Optimisation and Calculus of Variations, vol.12, issue.2, pp.311-349, 2006.
DOI : 10.1051/cocv:2006004

D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, 1991.
DOI : 10.1137/1.9781611970425

M. Gugat and G. Leugering, -Norm minimal control of the wave equation: on the weakness of the bang-bang principle, ESAIM: Control, Optimisation and Calculus of Variations, vol.14, issue.2, pp.254-283, 2008.
DOI : 10.1051/cocv:2007044

URL : https://hal.archives-ouvertes.fr/hal-01307221

E. Hernández, D. Kalise, and E. Otárola, Numerical approximation of the LQR problem in??a??strongly damped wave equation, Computational Optimization and Applications, vol.47, issue.2, pp.161-178, 2010.
DOI : 10.1007/s10589-008-9213-6

E. Hernández, D. Kalise, and E. Otárola, A locking-free scheme for the LQR control of a Timoshenko beam, Journal of Computational and Applied Mathematics, vol.235, issue.5, pp.1383-1393, 2011.
DOI : 10.1016/j.cam.2010.08.025

. Ishii, Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations, Indiana Univ, Math. J, vol.33, issue.5, pp.721-748, 1984.

K. Ito, On the regularity of solutions of an operator Riccati equation arising in linear quadratic optimal control problems for hereditary differential systems, Journal of Mathematical Analysis and Applications, vol.140, issue.2, pp.396-406, 1989.
DOI : 10.1016/0022-247X(89)90073-5

M. Jensen and I. Smears, On the Convergence of Finite Element Methods for Hamilton--Jacobi--Bellman Equations, SIAM Journal on Numerical Analysis, vol.51, issue.1, pp.137-162, 2013.
DOI : 10.1137/110856198

A. Kröner and K. Kunisch, A minimum effort optimal control problem for the wave equation, Computational Optimization and Applications, vol.47, issue.2, 2013.
DOI : 10.1007/s10589-013-9587-y

A. Kröner, K. Kunisch, and B. Vexler, Semismooth Newton Methods for Optimal Control of the Wave Equation with Control Constraints, SIAM Journal on Control and Optimization, vol.49, issue.2, pp.830-858, 2011.
DOI : 10.1137/090766541

K. Kunisch, S. Volkwein, and L. Xie, HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems, SIAM Journal on Applied Dynamical Systems, vol.3, issue.4, pp.701-722, 2004.
DOI : 10.1137/030600485

K. Kunisch and D. Wachsmuth, On time optimal control of the wave equation, its regularization and optimality system, ESAIM: Control, Optimisation and Calculus of Variations, vol.19, issue.2, pp.317-336, 2013.
DOI : 10.1051/cocv/2012010

K. Kunisch and L. Xie, POD-based feedback control of the burgers equation by solving the evolutionary HJB equation, Computers & Mathematics with Applications, vol.49, issue.7-8, pp.1113-1126, 2005.
DOI : 10.1016/j.camwa.2004.07.022

I. Lasiecka and R. Triggiani, Differential and Algebraic Riccati Equations with Applications to Boundary/Point Control Problems: Continuous Theory and Approximation Theory, p.160, 1991.
DOI : 10.1007/BFb0006880

J. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, 1972.

V. Mehrmann and H. Xu, Explicit Solutions for a Riccati Equation from Transport Theory, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.4, pp.1339-1357, 2008.
DOI : 10.1137/070708743

S. Osher and C. Shu, High-Order Essentially Nonoscillatory Schemes for Hamilton???Jacobi Equations, SIAM Journal on Numerical Analysis, vol.28, issue.4, pp.907-922, 1991.
DOI : 10.1137/0728049

A. Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion, Journal of Computational Physics, vol.54, issue.3, pp.468-488, 1984.
DOI : 10.1016/0021-9991(84)90128-1

J. P. Raymond, Feedback Boundary Stabilization of the Two-Dimensional Navier--Stokes Equations, SIAM Journal on Control and Optimization, vol.45, issue.3, pp.790-828, 2005.
DOI : 10.1137/050628726

URL : https://hal.archives-ouvertes.fr/hal-00629816

J. A. Sethian, Fast marching methods, SIAM Rev, pp.119-235, 1999.

E. Zuazua, Exact controllability for semilinear wave equations in one space dimension, Annales de l'I.H.P. section, pp.109-129, 1993.