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Journal of Convex Analysis 18 (2011), No. 3, 645--671
Copyright Heldermann Verlag 2011

Guarding a Line Segment

Beata Kraska
Institute of Mathematics and Computer Science, John Paul II Catholic University, ul. Konstantynów 1H, 20-708 Lublin, Poland

Witold Rzymowski
University of Technology, Nadbystrzycka 38 D, 20-618 Lublin, Poland

A line segment on the plane is guarded by a defender. An invader wants to pass through the line segment but he has to keep the distance from the defender no less than a given constant ρ > 0. The defender can move on the whole plane with maximal speed 1. The invader can move on the whole plane with maximal speed θ, greater than 1. No further kinematic or dynamic constraints are imposed on the defender and the invader motions. The maximal length of the line segment which can be guarded by the defender is established in this paper.

Keywords: Differential games, strategies, guarding territory problems

MSC: 49N70

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