Equivalence between Exact Internal Controllability of the Kirchhoff Plate-Like Equation and the Wave Equation

Abstract

When the rotatory inertia is taken into account, vibrations of a linear plate can be described by the Kirchhoff plate equation. Consider this equation with locally distributed control forces and some boundary condition which is the simply supported boundary condition for a rectangular plate. In this paper, the authors establish exact controllability of the system in terms of the equivalence to exact internal controllability of the wave equation, by means of a frequency domain characterization of exact controllability introduced recently in [11].

Keywords

Kirchhoff plate equation / Locally distributed control / Exact controllability / Wave equation / Frequency domain condition / 93B05 / 35B37 / 35B40 / O231 / O175.21

References

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