With use of the method of spherical means we are able to show that control processes modelled by the wave equation in a domain Ω ⊆ R n are exactly controllable in finite time by control forces applied at the boundary of the spatial region Ω. The introduction of certain concepts from harmonic analysis together with use of the Fourier transform enables us to apply this result to obtain finite time exact controllability theorems for processes modelled by the heat equation in the same region Ω with controls of the same type.
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David L. Russell (1973) studied this question.