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Approximate controllability for a linear modelof fluid structure interaction

Published online by Cambridge University Press:  15 August 2002

Axel Osses and
Jean-Pierre Puel
Axel Osses
Affiliation:
Universidad de Chile, Departamento de Ingeniería Matemática, Casilla 170/3, Correo 3, Santiago, Chile; axosses@dim.uchile.cl.
Jean-Pierre Puel
Affiliation:
Université de Versailles Saint-Quentin and Centre de Ma thé ma ti ques Appliquées, École Polytechnique, 91128 Palaiseau Cedex, France; jppuel@cmapx.polytechnique.fr.
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Abstract

We consider a linear model of interaction between a viscous incompressiblefluid and a thin elastic structure located on a part of the fluid domainboundary, the other part being rigid. After having given an existence anduniqueness result for the direct problem, we study the question ofapproximate controllability for this system when the control acts as anormal force applied to the structure. The case of an analytic boundary hasbeen studied by Lions and Zuazua in [9] where, in particular, a counterexample is givenwhen the fluid domain is a ball. We prove a result of approximatecontrollability in the 2d-case when the rigid and the elastic parts of theboundary make a rectangular corner and if the control acts on the wholeelastic structure.

Keywords

Controllabilityfluid-structure interactionnonsmooth domainsunique continuation property.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999, pp. 497 - 513
Copyright
© EDP Sciences, SMAI, 1999

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