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.

In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form $\frac{\partial y}{\partial n}+\beta \phantom{\rule{0.166667em}{0ex}}y=0$. We consider distributed controls with support in a small set and nonregular coefficients $\beta =\beta \left(x,t\right)$. 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 : https://doi.org/10.1051/cocv:2006010
Classification : 35K20,  93B05
Mots clés : 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},
zbl = {1106.93009},
mrnumber = {2224822},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2006010/}
}
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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