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Null controllability of the heat equation withboundary Fourier conditions: the linear 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., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain; cara@us.es; manoloburgos@us.es; sguerrero@us.es
Manuel González-Burgos
Affiliation:
Dpto. E.D.A.N., Universidad de 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

In this paper, we prove the global null controllability ofthe linear heat equation completed with linear Fourierboundary conditions of the form ${\partial y\over\partial n} + \beta\,y = 0$ . We consider distributed controls with support in a small set andnonregular coefficients $\beta=\beta(x,t)$ . For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heatequation with nonhomogeneous Neumann boundary conditions.

Keywords

Controllabilityheat equationFourier conditions.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 3 , July 2006 , pp. 442 - 465
Copyright
© EDP Sciences, SMAI, 2006

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References

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