Vibrating strings with free ends (Q1119212)

The author considers the reachable set for a non-homogeneous vibrating string with a point load control. Applying the standard transformation the system is represented by a homogeneous second order derivative - plus a multiplication operator. It is shown that the eigenelements of this operator under general regular boundary conditions constitute a Riesz base in the closure of their \(L_ 2\)-span. Then the author generalizes a result by \textit{I. Joo} [Stud. Sci. Math. Hung. 22, No.1-4, 1-9 (1987; Zbl 0657.93006)], to the more general setting. In particular, for almost all support points of the control, the reachable set increases for a time less than the minimum time for exact boundary reachability and is closed in the energy space.