A unified boundary controllability theory for hyperbolic and parabolic distributed parameter systems

By making use of Huyghen´s principle we are able to show that processes modelled by the wave equation in an odd number of space variables are controllable in finite time by means of control forces applied at the boundary of the spatial region in question. The introduction of certain concepts from harmonic analysis together with use of the Fourier transform enables us to apply this result to prove the finite time controllability of processes modelled by the heat equation in the same spatial region by means of similar boundary controls.