J. Dardé and S. Ervedoza, On the reachable set for the one-dimensional heat equation, SIAM J. Control Optim, vol.56, issue.3, pp.1692-1715, 2018.

P. Duchateau and F. Trèves, An abstract Cauchy-Kowaleska theorem in scales of Gevrey classes, Symposia Math, vol.7, pp.135-163, 1971.

W. Dunbar, N. Petit, P. Rouchon, and P. Martin, Motion planning for a nonlinear Stefan problem, ESAIM-COCV, vol.9, pp.275-296, 2003.

O. Y. Emanuvilov, Controllability of parabolic equations, Mat. Sb, vol.186, issue.6, pp.109-132, 1995.

A. V. Fursikov, O. Yu, and . Imanuvilov, Controllability of Evolution Equations, vol.34, 1996.

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

A. Hartmann, K. Kellay, and M. Tucsnak, From the reachable space of the heat equation to Hilbert spaces of homorphic functions

T. Kano and T. Nishida, Sur les ondes de surfaces de l'eau avec une justification mathématique deséquationsdes´deséquations des ondes en eau peu profonde, J. Math. Kyoto Univ, vol.19, issue.2, pp.335-370, 1979.

M. Kawagishi and T. Yamanaka, On the Cauchy problem for non linear PDEs in the Gevrey class with shrinkings, J. Math. Soc. Japan, vol.54, issue.3, pp.649-677, 2002.

D. Kinderlehrer and L. Nirenberg, Analyticity at the boundary of solutions of nonlinear second-order parabolic equations, Communications on Pure and Applied Mathematics, vol.31, pp.283-338, 1978.

B. Laroche, P. Martin, and P. Rouchon, Motion planning for the heat equation, Internat. J. Robust Nonlinear Control, vol.10, issue.8, pp.629-643, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01958371

W. Littman and S. Taylor, The heat and Schrödinger equations: boundary control with one shot, Control methods in PDE-dynamical systems, vol.426, pp.293-305, 2007.

P. Martin, I. Rivas, L. Rosier, and P. Rouchon, Exact controllability of a linear Korteweg-de Vries equation by the flatness approach
URL : https://hal.archives-ouvertes.fr/hal-01767971

P. Martin, L. Rosier, and P. Rouchon, Null controllability of the heat equation using flatness, Automatica, vol.50, pp.3067-3076, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00971484

P. Martin, L. Rosier, and P. Rouchon, Null controllability of one-dimensional parabolic equations by the flatness approach, SIAM J. Control Optim, vol.54, issue.1, pp.198-220, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01073404

P. Martin, L. Rosier, and P. Rouchon, On the reachable states for the boundary control of the heat equation, Appl. Math. Res. Express. AMRX, issue.2, pp.181-216, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01206378

P. Martin, L. Rosier, and P. Rouchon, Controllability of the 1D Schrödinger equation using flatness, Automatica, vol.91, pp.208-216, 2018.

T. Meurer, Control of higher-dimensional PDEs. Flatness and backstepping designs, Communications and Control Engineering Series, 2013.

L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Differential Geometry, vol.6, pp.561-576, 1972.

T. Nishida, A note on a theorem of Nirenberg, J. Differential Geometry, vol.12, pp.629-633, 1977.

H. Petzsche and E. On, Borel's theorem, Mathematische Annalen, vol.282, issue.2, pp.299-313, 1988.

W. Rudin, Principles of Mathematical Analysis, 1987.

B. Schörkhuber, T. Meurer, and A. , Flatness of semilinear parabolic PDEs-A Generalized Cauchy-Kowalevski Approach, IEEE Trans. Autom. Control, vol.58, issue.9, pp.2277-2291, 2013.

T. Yamanaka, A new higher order chain rule and Gevrey class, Ann. Global Anal. Geom, vol.7, issue.3, pp.179-203, 1989.

C. , S. Universitéuniversit´université, L. , ;. De-robotique, and M. Paristech, PARIS CEDEX 05, FRANCE E-mail address: camille.laurent@upmc.fr CENTRE AUTOMATIQUE ET SYST`EMESSYST` SYST`EMES (CAS), BOITE COURRIER, vol.187