F. Alabau-boussouira, J. Coron, and G. Olive, Internal Controllability of First Order Quasi-Linear Hyperbolic Systems with a Reduced Number of Controls, In : SIAM J. Control Optim, vol.55, pp.300-323, 2017.

P. Albano and D. Tataru, Carleman Estimates and Boundary Observability for a Coupled Parabolic-Hyperbolic System, In : Electron. J. Differential Equations, issue.22, p.15, 2000.

D. Allonsius, Etude spectrale d'opérateurs de Sturm-Liouville et applications à la contrôlabilité de problèmes paraboliques discrets et continus, 2018.

F. Khodja, A. Benabdallah, C. Dupaix, and I. Kostin, Null-Controllability of Some Systems of Parabolic Type by One Control Force, ESAIM : COCV 11.3 (juil. 2005), pp.426-448
URL : https://hal.archives-ouvertes.fr/hal-00474059

F. Khodja, A. Benabdallah, M. González-burgos, and L. De-teresa, Minimal Time for the Null Controllability of Parabolic Systems : The Effect of the Condensation Index of Complex Sequences, Journal of Functional Analysis, vol.267, pp.2077-2151, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00918596

F. Khodja, A. Benabdallah, M. González-burgos, and L. De-teresa, New Phenomena for the Null Controllability of Parabolic Systems : Minimal Time and Geometrical Dependence, Journal of Mathematical Analysis and Applications, vol.444, issue.2, pp.1071-1113
URL : https://hal.archives-ouvertes.fr/hal-01165713

F. Khodja, A. Benabdallah, M. González-burgos, and M. Morancey, Quantitative Fattorini-Hautus Test and Minimal Null Control Time for Parabolic Problems
URL : https://hal.archives-ouvertes.fr/hal-01557933

F. Ammar-khodja, A. Benabdallah, M. González-burgos, and L. De-teresa, Recent Results on the Controllability of Linear Coupled Parabolic Problems : A Survey, p.1305493, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01305493

J. Apraiz and L. Escauriaza, Null-Control and Measurable Sets, ESAIM : COCV 19.1 (jan. 2013), pp.239-254

J. Apraiz, L. Escauriaza, G. Wang, and C. Zhang, Observability Inequalities and Measurable Sets, J. Eur. Math. Soc, vol.16, issue.11, pp.2433-2475, 2014.

N. Arakelyan, On Efficient Analytic Continuation of Power Series, In : Math. USSR Sb, vol.52, pp.21-39, 1985.

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, vol.30, pp.1024-1065

K. Beauchard, Null Controllability of Kolmogorov-Type Equations, Math. Control Signals Syst. 26.1 (mar. 2014), pp.145-176
URL : https://hal.archives-ouvertes.fr/hal-00826117

K. Beauchard and P. Cannarsa, Heat Equation on the Heisenberg Group : Observability and Applications, Journal of Differential Equations, vol.262, pp.4475-4521

K. Beauchard, P. Cannarsa, and R. Guglielmi, Null Controllability of Grushin-Type Operators in Dimension Two, J. Eur. Math. Soc, vol.16, issue.1, pp.67-101, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00826116

K. Beauchard, J. Dardé, and S. Ervedoza, Minimal Time Issues for the Observability of Grushin-Type Equations, p.1677037, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01677037

K. Beauchard, B. Helffer, R. Henry, and L. Robbiano, Degenerate Parabolic Operators of Kolmogorov Type with a Geometric Control Condition, ESAIM : Control Optim. Calc. Var. 21.2 (avr. 2015), pp.487-512
URL : https://hal.archives-ouvertes.fr/hal-00863056

K. Beauchard, P. Jaming, and K. Pravda-starov, Spectral Inequality for Finite Combinations of Hermite Functions and Null-Controllability of Hypoelliptic Quadratic Equations. Avr, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01766300

K. Beauchard, A. Koenig, and K. L. Balc, Controllability of Linear Parabolic-Transport Systems. Juil. 2019. hal-02191017
URL : https://hal.archives-ouvertes.fr/hal-02191017

K. Beauchard, L. Miller, and M. Morancey, 2d Grushin-Type Equations : Minimal Time and Null Controllable Data, Journal of Differential Equations 259.11 (déc. 2015), pp.5813-5845

K. Beauchard and K. Pravda-starov, Null-Controllability of Hypoelliptic Quadratic Differential Equations, vol.5, pp.1-43, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01301604

K. Beauchard and E. Zuazua, Large Time Asymptotics for Partially Dissipative Hyperbolic Systems, Arch Rational Mech Anal, vol.199, issue.1, pp.177-227, 2011.

A. Benabdallah, F. Boyer, and M. Morancey, A Block Moment Method to Handle Spectral Condensation Phenomenon in Parabolic Control Problems, p.1949391, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01949391

F. Boyer, On the Penalised HUM Approach and Its Applications to the Numerical Approximation of Null-Controls for Parabolic Problems, CANUM 2012, 41e Congrès National d'Analyse Numérique. T. 41. ESAIM Proc. EDP Sci, vol.201, pp.15-58, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00812964

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, p.599, 2011.

J. Buchot and J. Raymond, Feedback Stabilization of a Boundary Layer Equation. II. Nonhomogeneous State Equations and Numerical Simulations, In : Appl. Math. Res. Express. AMRX, vol.2, pp.87-122, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00627459

F. W. Chaves-silva, L. Rosier, and E. Zuazua, Null Controllability of a System of Viscoelasticity with a Moving Control, Journal de Mathématiques Pures et Appliquées, vol.101, issue.2, pp.198-222, 2014.

J. B. Conway, Functions of One Complex Variable, Second. Graduate Texts in Mathematics, vol.11, 1978.

J. B. Conway, Functions of One Complex Variable. II. Graduate Texts in Mathematics 159, 1995.

J. Coron, Control and Nonlinearity. Mathematical Surveys and Monographs 143, 2007.

O. Costin and S. Garoufalidis, Resurgence of the Fractional Polylogarithms, Math. Res. Lett, vol.16, pp.817-826, 2009.

J. Dardé and S. Ervedoza, On the Reachable Set for the One-Dimensional Heat Equation, SIAM J. Control Optim, vol.56, pp.1692-1715, 2018.

E. B. Davies, Spectral Theory and Differential Operators. Cambridge Studies in Advanced Mathematics 42, 1995.

M. Dimassi and J. Sjöstrand, Spectral Asymptotics in the Semi-Classical Limit, London Mathematical Society Lecture Note Series, vol.268, 1999.

S. Dolecki, Observability for the One-Dimensional Heat Equation, Studia Math, vol.48, pp.291-305, 1973.

A. Doubova, E. Fernández-cara, M. González-burgos, and E. Zuazua, On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient, In : SIAM J. Control Optim, vol.41, pp.798-819, 2002.

M. Duprez, Controllability of a 2 × 2 Parabolic System by One Force with Space-Dependent Coupling Term of Order One, ESAIM Control Optim. Calc. Var, vol.23, pp.1473-1498, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01174812

M. Duprez and A. Koenig, Control of the Grushin Equation : Non-Rectangular Control Region and Minimal Time, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01829294

. Bibliographie,

M. Duprez and P. Lissy, Indirect Controllability of Some Linear Parabolic Systems of m Equations with M?1 Controls Involving Coupling Terms of Zero or First Order, Journal de Mathématiques Pures et Appliquées, vol.106, pp.905-934, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01162108

M. Duprez and G. Olive, Compact Perturbations of Controlled Systems, In : Math. Control Relat. Fields, vol.8, pp.397-410, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01406540

M. Egidi and I. Veseli?, Sharp Geometric Condition for Null-Controllability of the Heat Equation on ? and Consistent Estimates on the Control Cost, Arch. Math. 111.1 (juil, pp.85-99, 2018.

H. O. Fattorini and D. L. Russell, Exact Controllability Theorems for Linear Parabolic Equations in One Space Dimension, In : Arch. Rational Mech. Anal, vol.43, pp.272-292, 1971.

E. Fernández-cara and E. Zuazua, The Cost of Approximate Controllability for Heat Equations : The Linear Case, Adv. Differential Equations, vol.5, pp.465-514, 2000.

A. V. Fursikov and O. Y. Imanuvilov, Controllability of Evolution Equations, Lecture Note Series, vol.34, 1996.

S. Guerrero and O. Y. Imanuvilov, Remarks on Non Controllability of the Heat Equation with Memory, ESAIM Control Optim. Calc. Var, vol.19, issue.1, pp.288-300, 2013.

A. Hartmann, K. Kellay, and M. Tucsnak, From the Reachable Space of the Heat Equation to Hilbert Spaces of Holomorphic Functions

B. Helffer, Spectral Theory and Its Applications. Cambridge Studies in Advanced Mathematics 139, 2013.

B. Helffer and F. Nier, Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians, 2005.

M. Hitrik and K. Pravda-starov, Eigenvalues and Subelliptic Estimates for Non-Selfadjoint Semiclassical Operators with Double Characteristics, Ann. L'institut Fourier, vol.63, pp.985-1032, 2013.

L. Hörmander, The Analysis of Linear Partial Differential Operators III. Classics in Mathematics, 2007.

T. Kato, Perturbation Theory for Linear Operators, Classics in Mathematics, vol.132, 1995.

A. Koenig, Inégalité Spectrale Pour l'opérateur de Grushin. Mémoire de M2. Non publié

A. Koenig, Non-Null-Controllability of the Fractional Heat Equation and of the Kolmogorov Equation, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01829289

A. Koenig, Non-Null-Controllability of the Grushin Operator in 2D, Comptes Rendus Mathematique, vol.355, pp.1215-1235
URL : https://hal.archives-ouvertes.fr/hal-01654043

O. Kovrijkine, Some Results Related to the Logvinenko-Sereda Theorem, Proc. Amer. Math. Soc, vol.129, pp.3037-3047, 2001.

J. Rousseau and G. Lebeau, On Carleman Estimates for Elliptic and Parabolic Operators. Applications to Unique Continuation and Control of Parabolic Equations, pp.712-747, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00351736

G. Lebeau and L. Robbiano, Contrôle Exact de l'équation de La Chaleur, Commun. Partial Differ. Equ, vol.20, issue.2, pp.335-356, 1995.

G. Lebeau, Introduction Aux Inégalités de Carleman, Control and Stabilization of Partial Differential Equations. Séminaires & Congrès 29, pp.51-92, 2015.

G. Lebeau and E. Zuazua, Null-Controllability of a System of Linear Thermoelasticity, Arch Rational Mech Anal 141.4 (avr. 1998), pp.297-329

E. Lindelöf, Le Calcul Des Résidus et Ses Applications à La Théorie Des Fonctions. Les Grands Classiques Gauthier-Villars

J. Éditions and . Gabay, , 1989.

A. Martinez, An Introduction to Semiclassical and Microlocal Analysis, vol.191, 2002.

R. Metzler and J. Klafter, The Restaurant at the End of the Random Walk : Recent Developments in the Description of Anomalous Transport by Fractional Dynamics, J. Phys. A : Math. Gen, vol.37, pp.161-208, 2004.

S. Micu and E. Zuazua, On the Controllability of a Fractional Order Parabolic Equation, SIAM J. Control Optim, vol.44, issue.6, pp.1950-1972, 2006.

L. Miller, A Direct Lebeau-Robbiano Strategy for the Observability of Heatlike Semigroups, Discrete Contin. Dyn. Syst. -Ser. B, vol.14, issue.4, pp.1465-1485, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00411846

L. Miller, On the Controllability of Anomalous Diffusions Generated by the Fractional Laplacian, In : Math. Control Signals Syst, vol.18, issue.3, pp.260-271, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00008809

L. Miller, Unique Continuation Estimates for the Laplacian and the Heat Equation on Non-Compact Manifolds, Math. Res. Lett, vol.12, issue.1, pp.37-47, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00003099

. Bibliographie,

M. Müller and D. Schleicher, How to Add a Non-Integer Number of Terms, and How to Produce Unusual Infinite Summations, Journal of Computational and Applied Mathematics. Proceedings of the Seventh International Symposium on Orthogonal Polynomials, Special Functions and Applications, vol.178, pp.347-360, 2005.

F. Nier and B. Helffer, Quantitative Analysis of Metastability in Reversible Diffusion Processes via a Witten Complex Approach : The Case with Boundary, p.2744, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00002744

J. Oesterlé, Polylogarithmes, Astérisque, vol.216, issue.762, pp.49-67, 1993.

O. A. Oleinik and V. N. Samokhin, Mathematical Models in Boundary Layer Theory. T. 15. Applied Mathematics and Mathematical Computation, 1999.

F. W. Olver, A. B. Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert et al., éd. NIST Digital Library of Mathematical Functions, 2019.

M. Orsoni, Reachable States and Holomorphic Function Spaces for the 1-D Heat Equation
URL : https://hal.archives-ouvertes.fr/hal-02275568

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. T. 44. Applied Mathematical Sciences, p.279, 1983.

J. Peetre, Another Approach to Elliptic Boundary Problems, Commun. Pure Appl. Math, vol.14, pp.711-731, 1961.

J. Rauch and M. Taylor, Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains, Indiana Univ. Math. J, vol.24, pp.79-86, 1974.

L. P. Rothschild and E. M. Stein, Hypoelliptic Differential Operators and Nilpotent Groups, Acta Math, vol.137, pp.247-320, 1976.

W. Rudin, Real and Complex Analysis. 3 e éd, 1986.

J. Sjöstrand, Singularités Analytiques Microlocales, Astérisque, 95. T. 95, pp.1-166, 1982.

I. M. Sokolov, J. Klafter, and A. Blumen, Fractional Kinetics, Physics Today, vol.55, issue.11, pp.48-54, 2002.

G. Tenenbaum and M. Tucsnak, New Blow-up Rates for Fast Controls of Schrödinger and Heat Equations, Journal of Differential Equations, vol.243, issue.1, pp.70-100

M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups. Birkhäuser Advanced Texts Basler Lehrbücher, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00590673

G. Wang, M. Wang, C. Zhang, and Y. Zhang, Observable Set, Observability, Interpolation Inequality and Spectral Inequality for the Heat Equation in ?, J. Math. Pures Appl, issue.9, pp.144-194, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01633333