T. Liu and T. Yang, Well-Posedness Theory for System of Hyperbolic Conservation Laws, Hyperbolic Problems: Theory, Numerics, Applications, pp.681-691, 1999.

. .. Global-approximate-stabilization, 3.2 Well-posedness and properties of the flow

H. Anfinsen and O. M. Aamo, Stabilization and tracking control of a time-variant linear hyperbolic PIDE using backstepping, Automatica, vol.116, p.108929, 2020.

R. E. Barnett, Judicial Review of Federal Laws: The Meaning of the Necessary and Proper Clause, Restoring the Lost Constitution, 2013.

, Video 8. Simulated time course of receptor activation upon stabilization of a small, ordered domain.

K. Saito, Débat. Proposition 14 of Book V of the Elements : A Proposition that remained a Local Lemma, Revue d'histoire des sciences, vol.47, issue.2, pp.273-284, 1994.

, Appendix 137 Alternate proof of Lemma 207.1, De Gruyter Expositions in Mathematics, pp.317-318, 2018.

C. Appendix, Appendix 137 Alternate proof of Lemma 207.1, De Gruyter Expositions in Mathematics, pp.317-318, 2018.

T. K. Mandal, Real-Time Monitoring and Prediction of the Pilot Vehicle System (PVS) Closed-Loop Stability, Introduction A very classical problem for controllable system is the asymptotic stabilization issue

S. Xu, S. Cheng, and Z. Zhou, Reich?s iterated function systems and well-posedness via fixed point theory, Fixed Point Theory and Applications, vol.2015, issue.1, 2015.

. As-for-y,-we-have-?-±-?-t-m and . Let, We Have Work to Do Let’s Pull Together, Energy Engineering, vol.98, issue.3, pp.5-5, 2001.

R. Bibliography-;-fatiha-alabau-boussouira, O. Brockett, J. L. Glass, E. Rousseau, and . Zuazua, Lectures from the CIME Course held in Cetraro, Fondazione CIME/CIME Foundation Subseries, vol.2048, 2010.

J. Auriol and F. Di-meglio, Minimum time control of heterodirectional linear coupled hyperbolic PDEs, Automatica, vol.71, pp.300-307, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01215600

F. Ancona and A. Marson, On the Attainable Set for Scalar Nonlinear Conservation Laws with Boundary Control, SIAM Journal on Control and Optimization, vol.36, issue.1, pp.290-312, 1998.

A. A. Agrachev and A. V. Sarychev, Navier?Stokes Equations: Controllability by Means of Low Modes Forcing, Journal of Mathematical Fluid Mechanics, vol.7, issue.1, pp.108-152, 2005.

A. A. Agrachev and A. V. Sarychev, Controllability of 2D Euler and Navier-Stokes Equations by Degenerate Forcing, Communications in Mathematical Physics, vol.265, issue.3, pp.673-697, 2006.

J. Aubin, Un théorème de compacité, C. R. Acad. Sci, vol.256, pp.5042-5044, 1963.

M. Badra, Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system, ESAIM: Control, Optimisation and Calculus of Variations, vol.15, issue.4, pp.934-968, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00865811

V. Barbu, Stabilization of Navier?Stokes Flows, Stabilization of Navier?Stokes Flows, pp.87-175, 2011.

V. Barbu, Preliminaries, Controllability and Stabilization of Parabolic Equations, pp.1-26, 2018.

/. Birkhäuser and . Springer, , 2018.

M. Dejan, A. Bo?kovi?, M. Balogh, and . Krsti?, Backstepping in infinite dimension for a class of parabolic distributed parameter systems, Math. Control Signals Systems, vol.16, issue.1, pp.44-75, 2003.

K. Beauchard and J. Coron, Controllability of a quantum particle in a moving potential well, Journal of Functional Analysis, vol.232, issue.2, pp.328-389, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00825517

G. Bastin and J. Coron, Hyperbolic Systems of Balance Laws, Stability and Boundary Stabilization of 1-D Hyperbolic Systems, vol.88, pp.1-54, 2016.

G. Bastin, J. Coron, A. Hayat, and P. Shang, Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation, Mathematical Models and Methods in Applied Sciences, vol.29, issue.02, pp.271-316, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01723361

K. Beauchard, J. M. Coron, M. Mirrahimi, and P. Rouchon, Implicit Lyapunov control of finite dimensional Schrödinger equations, Systems & Control Letters, vol.56, issue.5, pp.388-395, 2007.

K. Beauchard, Local controllability of a 1-D Schrödinger equation, Journal de Mathématiques Pures et Appliquées, vol.84, issue.7, pp.851-956, 2005.

I. Christopher, A. Byrnes, and . Isidori, New results and examples in nonlinear feedback stabilization, Systems Control Lett, vol.12, issue.5, pp.437-442, 1989.

C. Bardos, G. Lebeau, and J. Rauch, 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.

V. Barbu, I. Lasiecka, and R. Triggiani, Abstract settings for tangential boundary stabilization of Navier?Stokes equations by high- and low-gain feedback controllers, Nonlinear Analysis: Theory, Methods & Applications, vol.64, issue.12, pp.2704-2746, 2006.

V. Barbu, I. Lasiecka, and R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations, Memoirs of the American Mathematical Society, vol.181, issue.852, pp.0-0, 2006.

K. Beauchard and M. Morancey, Local controllability of 1D Schrödinger equations with bilinear control and minimal time, Mathematical Control & Related Fields, vol.4, issue.2, pp.125-160, 2014.

J. Boussinesq, Essai sur la théorie des eaux courantes. Mémoires présentés par divers savantsà l'Acad, des Sci. Inst. Nat. France, XXIII, pp.1-680, 1877.

R. W. Brockett, Asymptotic stability and feedback stabilization, Differential geometric control theory, vol.27, pp.181-191, 1982.

J. L. Bona and R. Smith, The initial-value problem for the Korteweg-de Vries equation, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol.278, issue.1287, pp.555-601, 1975.

J. L. Bona, S. M. Sun, and B. Zhang, A Nonhomogeneous Boundary-Value Problem for the Korteweg?de Vries Equation Posed on a Finite Domain, Communications in Partial Differential Equations, vol.28, issue.7-8, pp.1391-1436, 2003.

J. L. Bona, S. M. Sun, and B. Zhang, A non-homogeneous boundary-value problem for the Korteweg?de Vries equation posed on a finite domain II, Journal of Differential Equations, vol.247, issue.9, pp.2558-2596, 2009.

M. Badra and T. Takahashi, Stabilization of Parabolic Nonlinear Systems with Finite Dimensional Feedback or Dynamical Controllers: Application to the Navier?Stokes System, SIAM Journal on Control and Optimization, vol.49, issue.2, pp.420-463, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00431041

T. Carleman, Sur un problème d'unicité pur les systèmes d'équations aux dérivées partiellesà deux variables indépendantes, Ark. Mat., Astr. Fys, vol.26, issue.17, p.9, 1939.

J. Coron and G. Bastin, Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm, SIAM Journal on Control and Optimization, vol.53, issue.3, pp.1464-1483, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01449620

J. Coron and G. Bastin, Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm, SIAM Journal on Control and Optimization, vol.53, issue.3, pp.1464-1483, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01449620

J. Coron, G. Bastin, and B. D'andréa-novel, Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1460-1498, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00923596

J. Coron and E. Crépeau, Exact boundary controllability of a nonlinear KdV equation with critical lengths, Journal of the European Mathematical Society, vol.6, issue.3, pp.367-398, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00077038

E. Cerpa and E. Crépeau, Boundary controllability for the nonlinear Korteweg?de Vries equation on any critical domain, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.2, pp.457-475, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00678473

E. Cerpa and E. Crépeau, Rapid exponential stabilization for a linear Korteweg-de Vries equation, Discrete & Continuous Dynamical Systems - B, vol.11, issue.3, pp.655-668, 2009.

E. Cerpa and J. Coron, Rapid Stabilization for a Korteweg-de Vries Equation From the Left Dirichlet Boundary Condition, IEEE Transactions on Automatic Control, vol.58, issue.7, pp.1688-1695, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00730190

J. Chu, J. Coron, and P. Shang, Asymptotic stability of a nonlinear Korteweg?de Vries equation with critical lengths, Journal of Differential Equations, vol.259, issue.8, pp.4045-4085, 2015.

J. Chu, J. Coron, P. Shang, and S. Tang, Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation, Chinese Annals of Mathematics, Series B, vol.39, issue.2, pp.201-212, 2018.

J. Coron and B. D'andrea-novel, Stabilization of a rotating body beam without damping, IEEE Transactions on Automatic Control, vol.43, issue.5, pp.608-618, 1998.

S. Chowdhury and S. Ervedoza, Open loop stabilization of incompressible navier-stokes equations in a 2d channel with a normal control using power series expansion, 2017.

E. Cerpa, Exact controllability of a nonlinear Korteweg-de Vries equation on a critical spatial domain, SIAM J. Control Optim, vol.46, issue.3, pp.877-899, 2007.

E. Cerpa, Control of a Korteweg-de Vries equation: A tutorial, Mathematical Control & Related Fields, vol.4, issue.1, pp.45-99, 2014.

J. Coron and A. V. Fursikov, Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary, Russian J. Math. Phys, vol.4, issue.4, pp.429-448, 1996.

A. Roberto, F. A. Capistrano-filho, and . Gallego, Asymptotic behavior of Boussinesq system of KdV-KdV type, J. Differential Equations, vol.265, issue.6, pp.2341-2374, 2018.

A. Roberto, A. F. Capistrano-filho, L. Pazoto, and . Rosier, Internal controllability of the Korteweg-de Vries equation on a bounded domain, ESAIM Control Optim. Calc. Var, vol.21, issue.4, pp.1076-1107, 2015.

J. Coron, L. Gagnon, and M. Morancey, Rapid stabilization of 1-D linear Schrödinger equations, 2016.

M. Chapouly, Global controllability of a nonlinear Korteweg-de Vries equation, Commun. Contemp. Math, vol.11, issue.3, pp.495-521, 2009.

M. Chapouly, Global Controllability of Nonviscous and Viscous Burgers-Type Equations, SIAM Journal on Control and Optimization, vol.48, issue.3, pp.1567-1599, 2009.

M. Chapouly, On the global null controllability of a Navier-Stokes system with Navier slip boundary conditions, J. Differential Equations, vol.247, issue.7, pp.2094-2123, 2009.

J. Coron, L. Hu, and G. Olive, Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation, Automatica J. IFAC, vol.84, pp.95-100, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01437107

W. Craig, T. Kappeler, and W. Strauss, Gain of regularity for equations of KdV type, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.9, issue.2, pp.147-186, 1992.

J. Coron and P. Lissy, Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components, Invent. Math, vol.198, issue.3, pp.833-880, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00750249

J. Coron and Q. Lü, Local rapid stabilization for a Korteweg-de Vries equation with a Neumann boundary control on the right, J. Math. Pures Appl, vol.102, issue.9, pp.1080-1120, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00905091

J. Coron and Q. Lü, Fredholm transform and local rapid stabilization for a Kuramoto-Sivashinsky equation, J. Differential Equations, vol.259, issue.8, pp.3683-3729, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01449589

H. Francis, Y. S. Clarke, E. D. Ledyaev, A. I. Sontag, and . Subbotin, Asymptotic controllability implies feedback stabilization, IEEE Trans. Automat. Control, vol.42, issue.10, pp.1394-1407, 1997.

J. Coron, F. Marbach, and F. Sueur, Small time global exact controllability of the Navier-Stokes equation with Navier slip-with-friction boundary conditions, J. Eur. Math. Soc. (JEMS), 2016.
URL : https://hal.archives-ouvertes.fr/hal-01422161

J. Coron, F. Marbach, F. Sueur, and P. Zhang, Controllability of the Navier?Stokes Equation in a Rectangle with a Little Help of a Distributed Phantom Force, Annals of PDE, vol.5, issue.2, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01676663

J. Coron and H. Nguyen, Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach, Archive for Rational Mechanics and Analysis, vol.225, issue.3, pp.993-1023, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01228895

J. Coron, A necessary condition for feedback stabilization, Systems & Control Letters, vol.14, issue.3, pp.227-232, 1990.

J. Coron, Global asymptotic stabilization for controllable systems without drift, Mathematics of Control, Signals, and Systems, vol.5, issue.3, pp.295-312, 1992.

J. Coron, Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C. R. Acad. Sci. Paris Sér. I Math, vol.317, issue.3, pp.271-276, 1993.

J. Coron, On the Stabilization in Finite Time of Locally Controllable Systems by Means of Continuous Time-Varying Feedback Law, SIAM Journal on Control and Optimization, vol.33, issue.3, pp.804-833, 1995.

J. Coron, On the controllability of 2-D incompressible perfect fluids, J. Math. Pures Appl, vol.75, issue.9, pp.155-188, 1996.

J. Coron, On the Null Asymptotic Stabilization of the Two-Dimensional Incompressible Euler Equations in a Simply Connected Domain, SIAM Journal on Control and Optimization, vol.37, issue.6, pp.1874-1896, 1999.

J. Coron, Control and Nonlinearity, Mathematical Surveys and Monographs, vol.136, 2009.

J. Coron, Some open problems on the control of nonlinear partial differential equations, Perspectives in nonlinear partial differential equations, vol.446, pp.215-243, 2007.

J. Coron, Phantom tracking method, homogeneity and rapid stabilization, Mathematical Control & Related Fields, vol.3, issue.3, pp.303-322, 2013.

J. Coron and L. Praly, Adding an integrator for the stabilization problem, Systems & Control Letters, vol.17, issue.2, pp.89-104, 1991.

J. Coron, On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions, ESAIM: Control, Optimisation and Calculus of Variations, vol.1, pp.35-75, 1996.

J. Coron and L. Praly, Adding an integrator for the stabilization problem, Systems & Control Letters, vol.17, issue.2, pp.89-104, 1991.

J. Coron and L. Rosier, On the stabilization of controllable and observable systems by an output feedback law, Mathematics of Control, Signals, and Systems, vol.7, issue.3, pp.187-216, 1994.

J. Coron and I. Rivas, Quadratic Approximation and Time-Varying Feedback Laws, SIAM Journal on Control and Optimization, vol.55, issue.6, pp.3726-3749, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01402747

J. Coron, I. Rivas, and S. Xiang, Local exponential stabilization for a class of Korteweg?de Vries equations by means of time-varying feedback laws, Analysis & PDE, vol.10, issue.5, pp.1089-1122, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01467008

P. Constantin and J. Saut, Local smoothing properties of dispersive equations, Journal of the American Mathematical Society, vol.1, issue.2, pp.413-413, 1988.

J. Coron and E. Trélat, Global Steady-State Controllability of One-Dimensional Semilinear Heat Equations, SIAM Journal on Control and Optimization, vol.43, issue.2, pp.549-569, 2004.

J. Coron, R. Vazquez, M. Krstic, and G. Bastin, Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping, SIAM Journal on Control and Optimization, vol.51, issue.3, pp.2005-2035, 2013.

J. Coron and S. Xiang, Small-time global stabilization of the viscous Burgers equation with three scalar controls, p.1723188, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01723188

J. Diaz, Obstruction and some approximate controllability results for the Burgers equation and related problems, Control of partial differential equations and applications, vol.174, pp.63-76, 1994.

F. Di-meglio, R. Vazquez, and M. Krstic, Stabilization of a System of <formula formulatype="inline"> <tex Notation="TeX">$n+1$</tex></formula> Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input, IEEE Transactions on Automatic Control, vol.58, issue.12, pp.3097-3111, 2013.

F. M. Gleb-germanovitch-doronin and . Natali, An example of non-decreasing solution for the KdV equation posed on a bounded interval, C. R. Math. Acad. Sci, vol.352, issue.5, pp.421-424, 2014.

S. Dolecki and D. L. Russell, A General Theory of Observation and Control, SIAM Journal on Control and Optimization, vol.15, issue.2, pp.185-220, 1977.

E. Fernández, -. Cara, and S. Guerrero, Null controllability of the Burgers system with distributed controls, Systems Control Lett, vol.56, issue.5, pp.366-372, 2007.

A. V. Fursikov and O. Y. Imanuvilov, On Controllability of Certain Systems Simulating a Fluid Flow, Flow Control, vol.68, pp.149-184, 1995.

A. V. Fursikov and O. Y. Imanuvilov, Controllability of evolution equations, Global Analysis Research Center, vol.34, 1996.

A. V. Fursikov and O. Y. Imanuvilov, Exact controllability of the Navier-Stokes and Boussinesq equations, Russian Mathematical Surveys, vol.54, issue.3, pp.565-618, 1999.

A. S. Fokas, Sixth SIAM conference on applied linear algebra: Final program and abstracts. Final technical report, CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.78, 1997.

H. O. Fattorini and D. L. Russell, Exact controllability theorems for linear parabolic equations in one space dimension, Archive for Rational Mechanics and Analysis, vol.43, issue.4, pp.272-292, 1971.

L. Gagnon, Lagrangian controllability of the Korteweg-de Vries equation with a higher order velocity field for the N-solitons solution, 2015 European Control Conference (ECC), 2015.
URL : https://hal.archives-ouvertes.fr/hal-01475391

O. Glass and S. Guerrero, On the Uniform Controllability of the Burgers Equation, SIAM Journal on Control and Optimization, vol.46, issue.4, pp.1211-1238, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00660830

O. Glass and S. Guerrero, Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit, Asymptotic Analysis, vol.60, issue.1-2, pp.61-100, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00139614

O. Glass and S. Guerrero, Controllability of the Korteweg?de Vries equation from the right Dirichlet boundary condition, Systems & Control Letters, vol.59, issue.7, pp.390-395, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00455223

C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for Solving the Korteweg-deVries Equation, Physical Review Letters, vol.19, issue.19, pp.1095-1097, 1967.

O. Glass and D. Han-kwan, On the controllability of the Vlasov?Poisson system in the presence of external force fields, Journal of Differential Equations, vol.252, issue.10, pp.5453-5491, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00590554

S. Guerrero and O. Y. Imanuvilov, Remarks on global controllability for the Burgers equation with two control forces, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.24, issue.6, pp.897-906, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00113443

O. Glass, Exact boundary controllability of 3-D Euler equation, ESAIM: Control, Optimisation and Calculus of Variations, vol.5, pp.1-44, 2000.

O. Glass, On the controllability of the Vlasov?Poisson system, Journal of Differential Equations, vol.195, issue.2, pp.332-379, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00590554

O. Glass, Asymptotic Stabilizability by Stationary Feedback of the Two-Dimensional Euler Equation: The Multiconnected Case, SIAM Journal on Control and Optimization, vol.44, issue.3, pp.1105-1147, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00020222

M. Gromov, SMOOTHING AND INVERSION OF DIFFERENTIAL OPERATORS, Mathematics of the USSR-Sbornik, vol.17, issue.3, pp.381-435, 1972.

M. Gromov, Singular Varieties: Complementary Results, Mixed Hodge Structures, vol.9, pp.141-159

, Die Bücher des Jahres 1912, Der Verlag von Julius Springer im Jahre 1912, pp.7-37, 1982.

O. Goubet and J. Shen, On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval, Adv. Differential Equations, vol.12, issue.2, pp.221-239, 2007.

I. M. Gel and G. E. , Theory of differential equations, Shilov. Generalized functions, vol.3, 2016.

I. M. Gel and N. Ya, Applications of harmonic analysis, Vilenkin. Generalized functions, vol.4, 1961.

L. Hörmander, On the Nash-Moser implicit function theorem, Annales Academiae Scientiarum Fennicae. Series A. I. Mathematica, vol.10, pp.255-259, 1985.

L. Hörmander, On the uniqueness of the Cauchy problem under partial analyticity assumptions, Geometrical Optics and Related Topics, vol.32, pp.179-219, 1997.

L. Hu, F. Di-meglio, R. Vazquez, and M. Krstic, Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs, IEEE Transactions on Automatic Control, vol.61, issue.11, pp.3301-3314, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01429825

. Lop-fat and . Ho, Observabilité frontière de l'équation des ondes, C. R. Acad. Sci. Paris Sér. I Math, vol.302, issue.12, pp.443-446, 1986.

T. Horsin, On the controllability of the Burger equation, ESAIM: Control, Optimisation and Calculus of Variations, vol.3, pp.83-95, 1998.

L. Hu, R. Vasquez, F. Di-meglio, and M. Krstic, Boundary exponential stabilization of 1-d inhomogeneous quasilinear hyperbolic systems, 2015.

C. Jia and B. Zhang, Boundary Stabilization of the Korteweg-de Vries Equation and the Korteweg-de Vries-Burgers Equation, Acta Applicandae Mathematicae, vol.118, issue.1, pp.25-47, 2012.

J. Diederik, G. Korteweg, and . De-vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag, vol.39, issue.5, pp.422-443, 1895.

D. E. Koditschek, Theoretical nuclear physics at Yale University, Proc. 5th. Yale University Conference, 1992.

V. Komornik, Rapid Boundary Stabilization of Linear Distributed Systems, SIAM Journal on Control and Optimization, vol.35, issue.5, pp.1591-1613, 1997.

M. Krstic, Compensating a String PDE in the Actuation or Sensing Path of an Unstable ODE, IEEE Transactions on Automatic Control, vol.54, issue.6, pp.1362-1368, 2009.

M. Krstic and A. Smyshlyaev, Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays, Systems & Control Letters, vol.57, issue.9, pp.750-758, 2008.

M. Krstic and A. Smyshlyaev, Boundary Control of PDEs, Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), vol.16, 2008.
URL : https://hal.archives-ouvertes.fr/hal-02931402

L. Ta-tsien, Global classical solutions for quasilinear hyperbolic systems, RAM: Research in Applied Mathematics. Masson, vol.32, 1994.

J. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Recherches en Mathématiques Appliquées, vol.2

P. Masson, , 1988.

W. Liu, Boundary Feedback Stabilization of an Unstable Heat Equation, SIAM Journal on Control and Optimization, vol.42, issue.3, pp.1033-1043, 2003.

W. Liu and M. Krsti?, Backstepping boundary control of Burgers? equation with actuator dynamics, Systems & Control Letters, vol.41, issue.4, pp.291-303, 2000.

W. Liu and M. Krsti?, Stability enhancement by boundary control in the Kuramoto?Sivashinsky equation, Nonlinear Analysis: Theory, Methods & Applications, vol.43, issue.4, pp.485-507, 2001.

J. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, Die Grundlehren der mathematischen Wissenschaften, vol.III, p.183, 1973.

J. Locker, Fredholm operators, Mathematical Surveys and Monographs, pp.41-82, 1999.

J. Locker, Eigenvalues and completeness for regular and simply irregular two-point differential operators, Memoirs of the American Mathematical Society, vol.195, issue.911, pp.0-0, 2008.

G. Lebeau and L. Robbiano, Contróle Exact De Léquation De La Chaleur, Communications in Partial Differential Equations, vol.20, issue.1-2, pp.335-356, 1995.

G. Lebeau and L. Robbiano, Contrôle exacte de l'équation de la chaleur, Séminaire sur lesÉquations aux Dérivées Partielles, 1994.

C. Laurent, L. Rosier, and B. Zhang, Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain, Communications in Partial Differential Equations, vol.35, issue.4, pp.707-744, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00386452

F. Marbach, An obstruction to small time local null controllability for a viscous Burgers' equation, Ann. Sci.Éc. Norm. Supér, issue.4
URL : https://hal.archives-ouvertes.fr/hal-01229493

F. Marbach, Small time global null controllability for a viscous Burgers' equation despite the presence of a boundary layer, Journal de Mathématiques Pures et Appliquées, vol.102, issue.2, pp.364-384, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00776508

S. Marx and E. Cerpa, Output feedback stabilization of the Korteweg?de Vries equation, Automatica, vol.87, pp.210-217, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01367650

M. Morancey, Simultaneous local exact controllability of 1D bilinear Schrödinger equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.31, issue.3, pp.501-529, 2014.

J. Moser, A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS, Proceedings of the National Academy of Sciences, vol.47, issue.11, pp.1824-1831, 1961.

J. Moser, A rapidly convergent iteration method and non-linear partial differential equations, vol.20, pp.265-315, 1966.

C. P. Massarolo, G. P. Menzala, and A. F. Pazoto, On the uniform decay for the Korteweg?de Vries equation with weak damping, Mathematical Methods in the Applied Sciences, vol.30, issue.12, pp.1419-1435, 2007.

A. Cohen and M. , Solutions of the Korteweg-de Vries equation from irregular data, Duke Math. J, vol.45, issue.1, pp.149-181, 1978.

M. A. Naimark, Spectral theory of differential operators, Spectral Theory of Linear Differential Operators and Comparison Algebras, pp.35-58, 1987.

M. A. Na?mark, Linear Differential Operators in a Hilbert Space, Linear Algebra and Linear Operators in Engineering - With Applications in Mathematica, pp.413-510, 2000.

J. Nash, The Imbedding Problem for Riemannian Manifolds, The Annals of Mathematics, vol.63, issue.1, p.20, 1956.

O. A. Oleinik and V. N. Samokhin, Mathematical Models in Boundary Layer Theory, Applied Mathematics and Mathematical Computation, vol.15, 2018.

G. Vassilis and . Papanicolaou, An example where separation of variables fails, J. Math. Anal. Appl, vol.373, issue.2, pp.739-744, 2011.

A. Fernando and P. , Unique continuation and decay for the Korteweg-de Vries equation with localized damping, ESAIM Control Optim. Calc. Var, vol.11, issue.3, pp.473-486, 2005.

V. Perrollaz, Exact Controllability of Scalar Conservation Laws with an Additional Control in the Context of Entropy Solutions, SIAM Journal on Control and Optimization, vol.50, issue.4, pp.2025-2045, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01108950

G. Menzala, C. F. Vasconcellos, and E. Zuazua, Stabilization of the Korteweg-de Vries Equation with localized damping, Q. Appl. Math., LX, issue.1, pp.111-129, 2002.

L. Prandtl, Uber Flüssigkeitsbewegung bei sehr kleiner Reibung, Verhaldlg II Int. Math. Kong, pp.484-491, 1904.

J. Raymond, Feedback Boundary Stabilization of the Two-Dimensional Navier--Stokes Equations, SIAM Journal on Control and Optimization, vol.45, issue.3, pp.790-828, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00629816

J. Raymond, Feedback boundary stabilization of the three-dimensional incompressible Navier?Stokes equations, Journal de Mathématiques Pures et Appliquées, vol.87, issue.6, pp.627-669, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00635929

L. Rosier, Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain, ESAIM: Control, Optimisation and Calculus of Variations, vol.2, pp.33-55, 1997.

L. Rosier, Control of the surface of a fluid by a wavemaker, ESAIM: Control, Optimisation and Calculus of Variations, vol.10, issue.3, pp.346-380, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00146833

D. L. Russell, Control theory of hyperbolic equations related to certain questions in harmonic analysis and spectral theory, Journal of Mathematical Analysis and Applications, vol.40, issue.2, pp.336-368, 1972.

I. Rivas, M. Usman, and B. Zhang, Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain, Mathematical Control & Related Fields, vol.1, issue.1, pp.61-81, 2011.

L. David, B. Y. Russell, and . Zhang, Smoothing and decay properties of solutions of the Korteweg-de Vries equation on a periodic domain with point dissipation, J. Math. Anal. Appl, vol.190, issue.2, pp.449-488, 1995.

L. David, B. Y. Russell, and . Zhang, Exact controllability and stabilizability of the Korteweg-de Vries equation, Trans. Amer. Math. Soc, vol.348, issue.9, pp.3643-3672, 1996.

L. Rosier and B. Zhang, Global Stabilization of the Generalized Korteweg--de Vries Equation Posed on a Finite Domain, SIAM Journal on Control and Optimization, vol.45, issue.3, pp.927-956, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00149689

L. Rosier and B. Zhang, Control and stabilization of the Korteweg-de Vries equation: recent progresses, Journal of Systems Science and Complexity, vol.22, issue.4, pp.647-682, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00600652

C. Samson, Velocity and torque feedback control of a nonholonomic cart, Advanced Robot Control, vol.162, pp.125-151

A. Smyshlyaev, E. Cerpa, and M. Krstic, Boundary Stabilization of a 1-D Wave Equation with In-Domain Antidamping, SIAM Journal on Control and Optimization, vol.48, issue.6, pp.4014-4031, 2010.

D. A. Smith and A. S. Fokas, Evolution PDEs and augmented eigenfunctions. Finite interval

A. A. ?kalikov, The completeness of eigenfunctions and associated functions of an ordinary differential operator with irregular-separated boundary conditions, Functional Analysis and Its Applications, vol.10, issue.4, pp.305-316, 1977.

M. Slemrod, A Note on Complete Controllability and Stabilizability for Linear Control Systems in Hilbert Space, SIAM Journal on Control, vol.12, issue.3, pp.500-508, 1974.

E. D. Sontag and H. J. Sussmann, Remarks on continuous feedback, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, pp.916-921, 1980.

J. Héctor and . Sussmann, Subanalytic sets and feedback control, J. Differential Equations, vol.31, issue.1, pp.31-52, 1979.

S. Tang, J. Chu, P. Shang, and J. Coron, Asymptotic stability of a Korteweg?de Vries equation with a two-dimensional center manifold, Advances in Nonlinear Analysis, vol.7, issue.4, pp.497-515, 2018.

R. Temam, Sur un problème non linéaire, J. Math. Pures Appl, vol.48, issue.9, pp.159-172, 1969.

E. Trélat, Contrôle optimal. Mathématiques Concrètes

P. Vuibert, Théorie & applications, 2005.

J. Tsinias, Sufficient lyapunov-like conditions for stabilization, Mathematics of Control, Signals, and Systems, vol.2, issue.4, pp.343-357, 1989.

M. Tucsnak and G. Weiss, Methods of Nonlinear Analysis, 2007.

S. Tang and C. Xie, State and output feedback boundary control for a coupled PDE?ODE system, Systems & Control Letters, vol.60, issue.8, pp.540-545, 2011.

J. Manuel-urquiza, Rapid exponential feedback stabilization with unbounded control operators, SIAM J. Control Optim, vol.43, issue.6, pp.2233-2244, 2005.

G. Beresford and W. , Pure and Applied Mathematics, 1999.

S. Xiang, Small-time local stabilization for a Korteweg?de Vries equation, Systems & Control Letters, vol.111, pp.64-69, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01723178

S. Xiang, Null Controllability of a Linearized Korteweg--de Vries Equation by Backstepping Approach, SIAM Journal on Control and Optimization, vol.57, issue.2, pp.1493-1515, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01468750

B. Zhang, Exact Boundary Controllability of the Korteweg--de Vries Equation, SIAM Journal on Control and Optimization, vol.37, issue.2, pp.543-565, 1999.

C. Zhang, Finite-time internal stabilization of a linear 1-D transport equation, Systems & Control Letters, vol.133, p.104529, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01980349

C. Zhang, Rapid stabilization of Burgers equations and of Korteweg-de Vries equations Abstract : This thesis is devoted to the study of stabilization of partial differential equations by nonlinear feedbacks. We are interested in the cases where classical linearization and stationary feedback law do not work for stabilization problems, for example KdV equations and Burgers equations. More precisely, it includes three important cases : stabilization of nonlinear systems whose linearized systems are not asymptotically stabilizable ; small-time local stabilization of linear controllable systems ; small-time global stabilization of nonlinear controllable systems. We find a strategy for the small-time global stabilization of the viscous Burgers equation : small-time global approximate stabilization and small-time local stabilization. Moreover, using a quadratic structure, Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback, 2018.

L. Zada and I. Aziz, The numerical solution of fractional Korteweg-de Vries and Burgers' equations via Haar wavelet, Stabilisation rapide d'équations de Burgers et de Korteweg-de, 2020.

M. Alamir, Une méthode du point fixe pour la mise en ?uvre de la commande prédictive non linéaire sous contraintes sur des EDP. Application à la stabilisation sous contraintes de l'équation aux dérivées partielles non linéaires de Kuramoto-Sivashinski, Journal Européen des Systèmes Automatisés, vol.45, issue.7-10, pp.693-713, 2011.