evasion from many pursuers on a compact and not necessarily convex set

In a given compact subset of r² 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 control are of coordinate-wise integral type. pursuers want to complete the pursuit and the evader is doing the opposite. completion of the pursuit means that the distance of evader becomes zero with some pursuers. some conditions for the completion of pursuit is derived.