# 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

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topFernández-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 -

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