On the global controllability of some evolutionary equations with an unbounded skew adjoint operator

We consider controlled initial-boundary value problems for semilinear partial differential equations with first- and second-order time derivatives, represented as a Cauchy problem for a semilinear evolution equation in a Hilbert space with an unbounded skew-adjoint operator and an incoming linear control function. Based on the author's previously obtained results for this Cauchy problem, sufficient conditions are established for the exact controllability of the equations under consideration to a given final state (as well as to given intermediate states at intermediate times) over an arbitrarily fixed (without additional conditions) time interval. Furthermore, a theorem on the stability of the control process is proved for an abstract evolution equation.