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On the convexity of reachability sets of controlled initial-boundary value problems. (English. Russian original) Zbl 1294.93018
Differ. Equ. 50, No. 5, 700-710 (2014); translation from Differ. Uravn. 50, No. 5, 702-712 (2014).
Summary: For a functional-operator equation describing a broad class of controlled initial-boundary value problems, we introduce the notion of abstract reachability set. We obtain sufficient conditions for the convexity and precompactness of that set. The situation of a Nash \(\varepsilon\)-equilibrium is justified in the sense of program strategies in noncooperative functional-operator games with many players. As an example of reduction of a controlled initial-boundary value problem to the equation under study, we consider the Cauchy problem for a semilinear wave equation with two space variables.

MSC:
93B03 Attainable sets, reachability
93C25 Control/observation systems in abstract spaces
91A10 Noncooperative games
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