A nonstationary group pursuit problem

We consider a linear nonstationary problem of conflict interaction of controllable objects, where the number of pursuers equals $\nu$ and the number of runaways equals $\mu$. All participants are assumed to have equal dynamic abilities. The purpose of the pursuers is to catch all runaways, while the purpose of the latter is to avoid the catch by at least one of them. We establish sufficient conditions for the solvability of a local evasion problem.