Winning conditions for evading into a circular region with speed advantage

In this study, we consider a two-player pursuit-evasion game in which an evader attempts to evade into a circular region while a pursuer along the boundary of this region aims at intercepting the evader. The evader is considered to possess a higher speed than that of the pursuer, which makes this study different from the existing ones. Both the players are assumed to have constant speeds and simple motions; that is, they can change their moving directions instantaneously. The sufficient conditions for the evader to win the game against the pursuer with a zero capture radius or a positive capture radius are proposed using geometric methods. In addition, both the evading strategies under the corresponding derived conditions against the pursuer are developed.