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On the convexity of reachability sets of controlled initial-boundary value problems

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Abstract

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 ɛ-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.

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Authors and Affiliations

  1. Nizhni Novgorod State Technical University, Nizhni Novgorod, Russia

    A. V. Chernov

  2. Nizhni Novgorod State University, Nizhni Novgorod, Russia

    A. V. Chernov

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  1. A. V. Chernov
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Correspondence to A. V. Chernov.

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Original Russian Text © A.V. Chernov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 5, pp. 702–712.

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Chernov, A.V. On the convexity of reachability sets of controlled initial-boundary value problems. Diff Equat 50, 700–710 (2014). https://doi.org/10.1134/S0012266114050127

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