ON EXACT GLOBAL CONTROLLABILITY OF A SEMILINEAR EVOLUTIONARY EQUATION WITH NONSTATIONARY OPERATOR

For a Cauchy problem associated with a controlled semilinear evolutionary equation with bounded nonstationary (id est depending on time) operator in a Hilbert space we obtain sufficient conditions for exact controllability to a given final state (and also to given intermediate states at intermediate time moments) on an arbitrarily fixed (without additional conditions) time interval. In fact, it is generalized an analogous result having been obtained by the author formerly for the case of a stationary operator. Like formerly, here we use the Minty–Browder’s theorem and also a chain technology of successive continuation of the solution to a controlled system to intermediate states. As example (of a specific interest) we consider a semilinear equation of the global electric circuit in the Earth atmosphere.