Abstract
For a nonlinear functional operator equation describing a wide class of controlled initial boundary-value problems we introduce the notion of an abstract reachability set analogous to the notion of a reachability tube. We obtain local sufficient conditions for the convexity of such a set. We consider a mixed boundary-value problem associated with a semilinear hyperbolic equation of the second order in a rather general form as an example illustrating the reduction of a controlled initial boundary-value problem to the studied equation, as well as the verification of the stated assumptions.
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