Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case

Enrique Fernández-Cara; Manuel González-Burgos; Sergio Guerrero; Jean-Pierre Puel

ESAIM: Control, Optimisation and Calculus of Variations (2006)

  • Volume: 12, Issue: 3, page 466-483
  • ISSN: 1292-8119

Abstract

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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 ∂ y ∂ n + f ( y ) = 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.

How to cite

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Fernández-Cara, Enrique, et al. "Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case." ESAIM: Control, Optimisation and Calculus of Variations 12.3 (2006): 466-483. <http://eudml.org/doc/249672>.

@article{Fernández2006,
abstract = { 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 $\{\partial y\over\partial n\} + f(y) = 0$. 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. },
author = {Fernández-Cara, Enrique, González-Burgos, Manuel, Guerrero, Sergio, Puel, Jean-Pierre},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Controllability; heat equation; Fourier boundary conditions; semilinear.; controllability; semilinear},
language = {eng},
month = {6},
number = {3},
pages = {466-483},
publisher = {EDP Sciences},
title = {Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case},
url = {http://eudml.org/doc/249672},
volume = {12},
year = {2006},
}

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
DA - 2006/6//
PB - EDP Sciences
VL - 12
IS - 3
SP - 466
EP - 483
AB - 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 ${\partial y\over\partial n} + f(y) = 0$. 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.
LA - eng
KW - Controllability; heat equation; Fourier boundary conditions; semilinear.; controllability; semilinear
UR - http://eudml.org/doc/249672
ER -

References

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  13. I. Lasiecka and R. Triggiani, Exact controllability of semilinear abstract systems with applications to waves and plates boundary control. Appl. Math. Optim.23 (1991) 109–154.  
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