Null controllability of the heat equation with boundary Fourier conditions : the linear case
Fernández-Cara, Enrique ; González-Burgos, Manuel ; Guerrero, Sergio1 ; Puel, Jean-Pierre2
1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France;
2 Laboratoire de Mathématiques Appliquées, Université de Versailles – St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; ; Laboratoire de Mathématiques Appliquées, Université de Versailles, St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France;
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 442-465.

In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form ∂y ∂n+βy=0. We consider distributed controls with support in a small set and nonregular coefficients β=β(x,t). For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.

DOI : 10.1051/cocv:2006010
Classification : 35K20, 93B05
Mots-clés : controllability, heat equation, Fourier conditions
Fernández-Cara, Enrique  ; González-Burgos, Manuel  ; Guerrero, Sergio 1 ; Puel, Jean-Pierre 2

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France;
2 Laboratoire de Mathématiques Appliquées, Université de Versailles – St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; ; Laboratoire de Mathématiques Appliquées, Université de Versailles, St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; 
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     title = {Null controllability of the heat equation with boundary {Fourier} conditions : the linear case},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {442--465},
     publisher = {EDP-Sciences},
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Fernández-Cara, Enrique; González-Burgos, Manuel; Guerrero, Sergio; Puel, Jean-Pierre. Null controllability of the heat equation with boundary Fourier conditions : the linear case. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 442-465. doi : 10.1051/cocv:2006010. http://www.numdam.org/articles/10.1051/cocv:2006010/

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