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

Published online by Cambridge University Press:  20 June 2006

Enrique Fernández-Cara ,
Manuel González-Burgos ,
Sergio Guerrero  and
Jean-Pierre Puel
Enrique Fernández-Cara
Affiliation:
Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain; cara@us.es; manoloburgos@us.es; sguerrero@us.es
Manuel González-Burgos
Affiliation:
Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain; cara@us.es; manoloburgos@us.es; sguerrero@us.es
Sergio Guerrero
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France; guerrero@ann.jussieu.fr
Jean-Pierre Puel
Affiliation:
Laboratoire de Mathématiques Appliquées, Université de Versailles – St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; jppuel@cmapx.polytechnique.fr
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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.

Keywords

Controllabilityheat equationFourier boundary conditionssemilinear.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 3 , July 2006 , pp. 466 - 483
Copyright
© EDP Sciences, SMAI, 2006

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