Geodesic
A~Game Problem on a~Closed Convex Set
Matematičeskie trudy, Tome 4 (2001) no. 2, pp. 96-112.

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The movements of Pursuer $P$ and Evader $E$ in ${\mathbb R}^n$ are described by the equations $P:\,\dot{x}=a(t)u$ and $E:\,\dot{y}=a(t)v$, where $u$ and $v$ are control parameters of $P$ and $E$. A closed convex subset $S$ of ${\mathbb R}^n$ is given. The players $P$ and $E$ must not leave $S$. Integral restrictions are imposed on the controls of the players. For arbitrary initial locations $x_0,y_0\in S$ of the players, the optimal time of pursuit is found and optimal strategies for the players are constructed. 
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G. I. Ibragimov. A~Game Problem on a~Closed Convex Set. Matematičeskie trudy, Tome 4 (2001) no. 2, pp. 96-112. http://geodesic.mathdoc.fr/item/MT_2001_4_2_a4/

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