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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; [email protected]; [email protected]; [email protected]
Manuel González-Burgos
Affiliation:
Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain; [email protected]; [email protected]; [email protected]
Sergio Guerrero
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France; [email protected]
Jean-Pierre Puel
Affiliation:
Laboratoire de Mathématiques Appliquées, Université de Versailles – St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; [email protected]
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Abstract

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