J. Aubin, Applied functional analysis, 1979.
DOI : 10.1002/9781118032725

V. Barbu, Exact Controllability of the Superlinear Heat Equation, Applied Mathematics and Optimization, vol.42, issue.1, pp.73-89, 2000.
DOI : 10.1007/s002450010004

A. Benabdallah, Y. Dermenjian, and J. L. Rousseau, Carleman estimates for the onedimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem. Preprint: LATP, Université d'Aix-Marseille I, www, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017486

A. Benabdallah, Y. Dermenjian, and J. L. Rousseau, Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient, and applications, Comptes Rendus M??canique, vol.334, issue.10, pp.582-586, 2006.
DOI : 10.1016/j.crme.2006.07.001

URL : https://hal.archives-ouvertes.fr/hal-00463326

A. Bressan, Hyperbolic systems of conservation laws, Revista Matem??tica Complutense, vol.12, issue.1, 2000.
DOI : 10.5209/rev_REMA.1999.v12.n1.17204

H. Brezis, Analyse fonctionnelle, 1983.

A. Doubova, E. Fernandez-cara, M. Gonzales-burgos, and E. Zuazua, On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient, SIAM Journal on Control and Optimization, vol.41, issue.3, pp.798-819, 2002.
DOI : 10.1137/S0363012901386465

A. Doubova, A. Osses, and J. Puel, Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients, ESAIM: Control, Optimisation and Calculus of Variations, vol.8, pp.621-661, 2002.
DOI : 10.1051/cocv:2002047

C. Fabre, J. Puel, and E. Zuazua, Approximate controllability of the semilinear heat equation, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.31, issue.01, pp.31-61, 1995.
DOI : 10.1007/978-1-4612-5561-1

E. Fernández-cara and S. Guerrero, Global Carleman Inequalities for Parabolic Systems and Applications to Controllability, SIAM Journal on Control and Optimization, vol.45, issue.4, pp.1395-1446, 2006.
DOI : 10.1137/S0363012904439696

E. Fernández-cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.17, issue.5, pp.583-616, 2000.
DOI : 10.1016/S0294-1449(00)00117-7

E. Fernández-cara and E. Zuazua, On the null controllability of the one-dimensional heat equation with BV coefficients, Comput. Appl. Math, vol.21, pp.167-190, 2002.

A. Fursikov, O. Yu, and . Imanuvilov, Controllability of evolution equations, Seoul National University, vol.34, 1996.

O. Y. Imanuvilov and M. Yamamoto, Carleman estimate for a parabolic equation in a Sobolev space of negative order and its applications, Lecture Notes in Pure and Applied Mathematics, vol.218, pp.113-137, 2001.
DOI : 10.1201/9780203904190.ch6

A. Kolmogorov and S. V. Fomin, Eléments de la théorie des fonctions et de l'analyse fonctionnelle, Editions MIR, 1974.

J. Lions, Quelques méthodes de résolution desprobì emes aux limites non linéaires. Dunod, 1969.

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, 1983.
DOI : 10.1007/978-1-4612-5561-1

D. L. Russell, A Unified Boundary Controllability Theory for Hyperbolic and Parabolic Partial Differential Equations, Studies in Applied Mathematics, vol.40, issue.3, pp.189-221, 1973.
DOI : 10.1002/sapm1973523189