F. Belgacem and S. Kaber, On the Dirichlet boundary controllability of the one-dimensional heat equation: semi-analytical calculations and ill-posedness degree, Inverse Problems, vol.27, issue.5, p.55012, 2011.
DOI : 10.1088/0266-5611/27/5/055012

F. Boyer, F. Hubert, and J. L. Rousseau, Uniform controllability properties for space/time-discretized parabolic equations, Numerische Mathematik, vol.59, issue.1, pp.601-661, 2011.
DOI : 10.1007/s00211-011-0368-1

URL : https://hal.archives-ouvertes.fr/hal-00429197

C. Carthel, R. Glowinski, and J. Lions, On exact and approximate boundary controllabilities for the heat equation: A numerical approach, Journal of Optimization Theory and Applications, vol.22, issue.3, pp.429-484, 1994.
DOI : 10.1007/BF02192213

H. Fattorini and D. 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.
DOI : 10.1007/BF00250466

E. Fernández-cara and A. Münch, Numerical null controllability of the 1D heat equation: primal methods. HAL preprint http, 2011.

M. Fliess, J. Lévine, P. Martin, and P. Rouchon, Flatness and defect of non-linear systems: introductory theory and examples, International Journal of Control, vol.4, issue.6, pp.611327-1361, 1995.
DOI : 10.1109/9.73561

A. V. Fursikov and O. Y. Imanuvilov, Controllability of evolution equations, 1996.

G. Garcia, A. Osses, and M. Tapia, A heat source reconstruction formula from single internal measurements using a family of null controls, Journal of Inverse and IIIposed Problems
DOI : 10.1515/jip-2011-0001

D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, 2001.

L. Hörmander, The analysis of linear partial differential operators. I, 1983.

B. Jr, A fundamental solution for the heat equation which is supported in a strip, J. Math. Anal. Appl, vol.60, issue.2, pp.314-324, 1977.

B. Laroche, P. Martin, and P. Rouchon, Motion planning for the heat equation, International Journal of Robust and Nonlinear Control, vol.59, issue.60, pp.629-643, 2000.
DOI : 10.1002/1099-1239(20000715)10:8<629::AID-RNC502>3.0.CO;2-N

G. Lebeau and L. Robbiano, Contr??le Exact De L??quation De La Chaleur, Communications in Partial Differential Equations, vol.52, issue.1-2, pp.335-356, 1995.
DOI : 10.1016/0022-0396(87)90043-X

Y. Guo and W. Littman, Null boundary controllability for semilinear heat equations, Appl Math Optim, vol.32, issue.3, pp.281-316, 1995.

]. W. Littman, Boundary control theory for hyperbolic and parabolic partial differential equations with constant coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.5, issue.43, pp.567-580, 1978.

W. Littman and S. Taylor, The heat and Schr??dinger equations: boundary control with one shot, Control methods in PDE-dynamical systems, pp.293-305, 2007.
DOI : 10.1090/conm/426/08194

W. A. Luxemburg and J. Korevaar, Entire functions and Müntz-Szász type approximation, Trans. Amer. Math. Soc, vol.157, pp.23-37, 1971.

A. Lynch and J. Rudolph, Flatness-based boundary control of a class of quasilinear parabolic distributed parameter systems, International Journal of Control, vol.11, issue.15, pp.1219-1230, 2002.
DOI : 10.1524/auto.2000.48.8.399

P. Martin, L. Rosier, and P. Rouchon, Null controllability of the 1D heat equation using flatness, 1st IFAC workshop on Control of Systems Governed by Partial Differential Equations (CPDE2013), 2013.
DOI : 10.3182/20130925-3-FR-4043.00074

URL : https://hal.archives-ouvertes.fr/hal-00971487

P. Martin, L. Rosier, and P. Rouchon, Null controllability of the 2D heat equation using flatness, 52nd IEEE Conference on Decision and Control, 2013.
DOI : 10.1109/CDC.2013.6760459

URL : https://hal.archives-ouvertes.fr/hal-01112044

T. Meurer, Flatness-based trajectory planning for diffusion???reaction systems in a parallelepipedon???A spectral approach, Automatica, vol.47, issue.5, pp.935-949, 2011.
DOI : 10.1016/j.automatica.2011.02.004

T. Meurer and M. Zeitz, Model inversion of boundary controlled parabolic partial differential equations using summability methods, Mathematical and Computer Modelling of Dynamical Systems, vol.8, issue.3, pp.213-230, 2008.
DOI : 10.1016/0167-7977(89)90011-7

S. Micu and E. Zuazua, Regularity issues for the null-controllability of the linear 1-d heat equation, Systems & Control Letters, vol.60, issue.6, pp.406-413, 2011.
DOI : 10.1016/j.sysconle.2011.03.005

A. Münch and E. Zuazua, Numerical approximation of null controls for the heat equation: Ill-posedness and remedies, Inverse Problems, vol.26, issue.8, p.85018, 2010.
DOI : 10.1088/0266-5611/26/8/085018

J. Ramis, Dévissage Gevrey, Journées Singulières de Dijon, pp.173-204, 1978.

J. Roe, Elliptic operators, topology and asymptotic methods, Pitman Research Notes in Mathematics Series. Longman, vol.395, 1998.

L. Rosier, A fundamental solution supported in a strip for a dispersive equation, Special issue in memory of Jacques-Louis Lions, pp.355-367, 2002.

W. Rudin, Real and complex analysis, 1987.

M. A. Shubin, Pseudodifferential operators and spectral theory, 2001.
DOI : 10.1007/978-3-642-56579-3

T. Yamanaka, A new higher order chain rule and gevrey class Annals of Global Analysis and Geometry, 31] C. Zheng. Controllability of the time discrete heat equation. Asymptotic Anal, pp.179-2033, 1989.

E. Zuazua, Control and numerical approximation of the wave and heat equations, In International Congress of Mathematicians. Eur. Math. Soc, vol.III, pp.1389-1417, 2006.
DOI : 10.4171/022-3/67