Boundary controllability problems for the wave equation in a parallelepiped Original Research Article

The wave equation in an N-dimensional parallelepiped with boundary control equal zero everywhere except of an edge of dimension N − 2 is considered. The other case which is investigated is the boundary control acting on a face of dimension N − 1 and depending on N − 1 independent variables (including t). It is proved that, in both cases, the system is not approximately controllable for any T > 0.