Geodesic
On a~pursuit-evasion problem under a~linear change of the pursuer resource
Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 159-171.

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We study a pursuit-evasion problem in the case when an integral constraint is imposed on the pursuer control class which is a generalization of integral as well as geometric constraints and only a geometric constraint is imposed on the evader control class. We prove the theorem of alternative. The optimal pursuit problem is solved by a generalized parallel pursuit strategy, and lower bounds for the distance between the pursuer and the evader are established in the pursuit problem. 
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B. T. Samatov. On a~pursuit-evasion problem under a~linear change of the pursuer resource. Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 159-171. http://geodesic.mathdoc.fr/item/MT_2012_15_2_a9/

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