Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 466-483.

This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form $\frac{\partial y}{\partial n}+f\left(y\right)=0$. We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one has exact controllability to the trajectories.

DOI : https://doi.org/10.1051/cocv:2006011
Classification : 35K20,  93B05
Mots clés : controllability, heat equation, Fourier boundary conditions, semilinear
@article{COCV_2006__12_3_466_0,
author = {Fern\'andez-Cara, Enrique and Gonz\'alez-Burgos, Manuel and Guerrero, Sergio and Puel, Jean-Pierre},
title = {Exact controllability to the trajectories of the heat equation with {Fourier} boundary conditions : the semilinear case},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {466--483},
publisher = {EDP-Sciences},
volume = {12},
number = {3},
year = {2006},
doi = {10.1051/cocv:2006011},
zbl = {1106.93010},
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Fernández-Cara, Enrique; González-Burgos, Manuel; Guerrero, Sergio; Puel, Jean-Pierre. Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 466-483. doi : 10.1051/cocv:2006011. http://www.numdam.org/articles/10.1051/cocv:2006011/

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