Geodesic
$\varepsilon$-positional strategies in the theory of differential pursuit games and the invariance of a constant multivalued mapping in the heat conductivity problem
Contemporary Mathematics. Fundamental Directions, Contemporary problems in mathematics and physics, Tome 65 (2019) no. 1, pp. 124-136

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In this paper, we consider two problems. In the first problem, we prove that if the assumption from the paper [1] and one additional condition on the parameters of the game hold, then the pursuit can be finished in any neighborhood of the terminal set. To complete the game, an $\varepsilon$-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 on the right-hand side. 
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     author = {M. Tukhtasinov and Kh. Ya. Mustapokulov},
     title = {$\varepsilon$-positional strategies in the theory of differential pursuit games and the invariance of a constant multivalued mapping in the heat conductivity problem},
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M. Tukhtasinov; Kh. Ya. Mustapokulov. $\varepsilon$-positional strategies in the theory of differential pursuit games and the invariance of a constant multivalued mapping in the heat conductivity problem. Contemporary Mathematics. Fundamental Directions, Contemporary problems in mathematics and physics, Tome 65 (2019) no. 1, pp. 124-136. http://geodesic.mathdoc.fr/item/CMFD_2019_65_1_a10/