Abstract
In this paper, we consider two problems. In the first problem, we prove that if the assumption from [1] and one additional condition on the parameters of the game hold, then the pursuit can be completed in any neighborhood of the terminal set. To complete the game, an ε-positional pursuit strategy is constructed.In the second problem, we study the invariance of a given multivalued mapping with respect to the system with distributed parameters. The system is described by the heat-conductivity equation containing additive control terms at the right-hand side.
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