Some problems in the theory of differential pursuit games in systems with distributed parameters

A game with dynamics described by partial differential equations is considered. The equations of the players are additively represented on the right-hand side and are subject to integral or pointwise restrictions. The goal of the first player, who is informed of the instantaneous value of the control of his partner, is to bring the system into an unperturbed state. To solve the problem the decomposition method developed in [1] for a controlled system (with one player) is used. Three combinations of restrictions on the players are considered. In all cases the control of the first player is presented explicitly. The main complication, compared with the problem considered previously [1] is that this control consists of two terms estimated in different norms.