Исследование одного класса задач оптимального управления подвижными источниками

The problem of optimal control of processes described by a parabolic type equation with moving sources is investigated in the paper. A theorem on existence and uniqueness of the solution is solved for the optimal control problem. Sufficients conditions of Frechet differentiability of quality test and an expression for its gradient are obtained, necessary conditions of optimality in the form of point wise and integral maximum principles are established for an optimal control problem.