Evasion from many Pursuers on a Compact and not Necessarily Convex Set

In a given compact subset of R۲ which is not necessarily convex, we study a pursuit differential game of many pursuers and one evader. The game must be done in this set. The constraints that we used for controls are coordinate-wise integral. Pursuers want to complete the pursuit and the evader is doing theopposite. Completion of the pursuit means that the distance of evader becomes zero with some pursuers. Some conditions for the completion of pursuit are derived.