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 . 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.
Keywords: controllability, heat equation, Fourier boundary conditions, semilinear
Fernández-Cara, Enrique ; González-Burgos, Manuel ; Guerrero, Sergio 1 ; Puel, Jean-Pierre 2
@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},
year = {2006},
publisher = {EDP Sciences},
volume = {12},
number = {3},
doi = {10.1051/cocv:2006011},
mrnumber = {2224823},
zbl = {1106.93010},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2006011/}
}
TY - JOUR AU - Fernández-Cara, Enrique AU - González-Burgos, Manuel AU - Guerrero, Sergio AU - Puel, Jean-Pierre TI - Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 466 EP - 483 VL - 12 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2006011/ DO - 10.1051/cocv:2006011 LA - en ID - COCV_2006__12_3_466_0 ER -
%0 Journal Article %A Fernández-Cara, Enrique %A González-Burgos, Manuel %A Guerrero, Sergio %A Puel, Jean-Pierre %T Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 466-483 %V 12 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2006011/ %R 10.1051/cocv:2006011 %G en %F COCV_2006__12_3_466_0
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
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