Game problems on a fixed interval in controlled first-order evolution equations

This paper is devoted to the study of pursuit and evasion problems on a fixed finite closed interval in controlled equations of parabolic type. The control parameters appear on the right-hand side of the equations in additive form. We study all possible cases of control constraints. For certain cases, we single out pairs of sets of initial positions for which the completion of the pursuit from points of the first set is guaranteed and an evasion of the terminal set is ensured in the case of initial points from the second set.