Some remarks on exact controllability of strings and beams with boundary controls in Lp(0,T), p⩾2

The problem of exact null controllability of normalized strings and beams subject to boundary controls in an L^p(0, T)-space, where p is larger than or equal to two, is discussed. In particular, the case of L^∞-controls is of great importance in the applications. It is shown that subtle questions about Fourier series come into play in this problem. In particular, dealing with beam related control problems, lacunary Fourier series play a dominant role; this refers to the notions of (p,q)-sets. Various results on exact controllability with L^p-controls of special string and beam models are given