To the non-stationary problem of the group pursuit with phase restrictions

In this article two linear non-stationary pursuit-evasion problems with one evader and the group of pursuers under condition of equivalent dynamic possibilities and that the evader can not leave the certain set are considered. It's proved that if the number of pursuers is less than the dimension of the space, then the evader can avoid meeting on the interval $[t_0,\infty)$.