Optimality Conditions in the Problem of Thermal Control with Integral-Differential Equation

The optimal control problem for thermal process described by Fredholm integral-differential equation is considered. The definition of the weak generalized solution of the boundary problem is given. The algorithm of its construction is presented. It was found that the optimal control should be found as the solution of nonlinear integral equations with additional conditions in the form of differential inequalities with respect to the source functions.