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In this paper we investigate a differential game in which countably manydynamical objects pursue a single one. All the players perform simple motions.The duration of the game is fixed. The controls of a group of pursuers aresubject to geometric constraints and the controls of the other pursuers and theevader are subject to integral constraints. The payoff of the game is thedistance between the evader and the closest pursuer when the game isterminated. We construct optimal strategies for players and find the value ofthe game.

On a fixed duration pursuit differential game with geometric and integral constraints