Exact controllability in fluid – solid structure: The Helmholtz model
Université Paul Sabatier,
UMR 5640, Laboratoire MIP, 31062 Toulouse Cedex 4, France; firstname.lastname@example.org
2 IISc-TIFR Mathematics Programme, TIFR Centre, Bangalore 560012, India.
Revised: 1 March 2004
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.
Mathematics Subject Classification: 35B37 / 93C20
Key words: Fluid – solid structure / exact controllability.
© EDP Sciences, SMAI, 2005