In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form . We consider distributed controls with support in a small set and nonregular coefficients . 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.
Keywords: controllability, heat equation, Fourier conditions
@article{COCV_2006__12_3_442_0, author = {Fern\'andez-Cara, Enrique and Gonz\'alez-Burgos, Manuel and Guerrero, Sergio and Puel, Jean-Pierre}, 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}, volume = {12}, number = {3}, year = {2006}, doi = {10.1051/cocv:2006010}, mrnumber = {2224822}, zbl = {1106.93009}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2006010/} }
TY - JOUR AU - Fernández-Cara, Enrique AU - González-Burgos, Manuel AU - Guerrero, Sergio AU - Puel, Jean-Pierre TI - Null controllability of the heat equation with boundary Fourier conditions : the linear case JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 442 EP - 465 VL - 12 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2006010/ DO - 10.1051/cocv:2006010 LA - en ID - COCV_2006__12_3_442_0 ER -
%0 Journal Article %A Fernández-Cara, Enrique %A González-Burgos, Manuel %A Guerrero, Sergio %A Puel, Jean-Pierre %T Null controllability of the heat equation with boundary Fourier conditions : the linear case %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 442-465 %V 12 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2006010/ %R 10.1051/cocv:2006010 %G en %F COCV_2006__12_3_442_0
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, Volume 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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