Abstract

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\varrho > 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.

Author information

Contact details are reproduced from the original publication and may be historical.

Beata Kraska

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

kraskab@kul.lublin.pl

Witold Rzymowski

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

Keywords

  • Differential games
  • strategies
  • guarding territory problems

Mathematics Subject Classification

49N70

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Suggested citation

B. Kraska, W. Rzymowski. “Guarding a Line Segment.” Journal of Convex Analysis 18 (2011), No. 3, 645–671. https://doi.org/10.68381/jca18041

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.