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Exact controllability in fluid – solid structure: The Helmholtz model

Published online by Cambridge University Press:  15 March 2005

Jean-Pierre Raymond  and
Muthusamy Vanninathan
Jean-Pierre Raymond
Affiliation:
Université Paul Sabatier, UMR 5640, Laboratoire MIP, 31062 Toulouse Cedex 4, France; raymond@mip.ups-tlse.fr
Muthusamy Vanninathan
Affiliation:
IISc-TIFR Mathematics Programme, TIFR Centre, Bangalore 560012, India.
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Abstract

A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results.

Keywords

Fluid – solid structureexact controllability.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 2 , April 2005 , pp. 180 - 203
Copyright
© EDP Sciences, SMAI, 2005

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