Geodesic
The method of tracking domains in search problems
Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 225-246

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A new, geometric approach to solving dynamical search problems is proposed. On the example of certain two-dimensional search problems it is shown how, using the method proposed, one can find sufficient conditions guaranteeing detection, as well as determining the corresponding trajectories and the necessary time. 
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     author = {A. G. Chkhartishvili and E. V. Shikin},
     title = {The method of tracking domains in search problems},
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A. G. Chkhartishvili; E. V. Shikin. The method of tracking domains in search problems. Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 225-246. http://geodesic.mathdoc.fr/item/SM_1995_80_1_a11/