Controllability of analytic functions for a wave equation coupled with a beam

Abstract

We consider the controllability and observation problem for a simple model describing the interaction between a fluid and a beam. For this model microlocal propagation of singularities proves that the space of controlled functions is smaller that the energy space. We use spectral properties and an explicit construction of biorthogonal sequences to show that analytic functions can be controlled within finite time. We also give an estimate for this time related to the amount of analyticity of the latter function.