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Exact controllability for a model of a multidimensional flexible structure

Published online by Cambridge University Press:  14 November 2011

Jean Pierre Puel  and
Enrique Zuazua
Jean Pierre Puel
Affiliation:
Departement de Mathématiques, Université d'Orléans; and Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France
Enrique Zuazua
Affiliation:
Departamento de Matemática Aplicada, Universidad Complutense, 28040 Madrid, Spain
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Synopsis

A simple model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional straight string is introduced. In both regions (n-dimensional body and a onedimensional string) the state is assumed to satisfy the wave equation. Simple boundary conditions are introduced at the junction. These conditions, in the absence of control, ensure conservation of the total energy of the system and imply some rigidity of the boundary of the n-d body on a neighbourhood of the junction. The exact boundary controllability of the system is proved by means of a Dirichlet control supported on a subset of the boundary of the n-d domain which excludes the junction region. Some extensions are discussed at the end of the paper.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 2 , 1993 , pp. 323 - 344
Copyright
Copyright © Royal Society of Edinburgh 1993

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