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....
In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a regular Bloch spectrum is not guaranteed. The aim here is to develop all necessary spectral tools to overcome...
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...
In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three
dimensions. The Bloch wave method for homogenization relies on the regularity of the
lower Bloch spectrum. For the three dimensional linear elasticity system,
the first eigenvalue is degenerate of multiplicity three and hence
existence of such a regular Bloch spectrum is guaranteed. The
aim here is to develop all necessary spectral tools to overcome...
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