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Sensitivity of optimal controls for time delay parabolic systems

The first order sensitivity analysis is performed for a class of optimal control problems for time delay parabolic equations in which retarded arguments appear in the integral form with h ϵ (0,6). The optimality system is analyzed with the respect to a small parameter. The directional derivative of the optimal control is obtained as a solution to an auxiliary optimization problem. The control constraints for the auxilary optimization problem are received.