Necessary optimality conditions in an optimal control problem for a parabolic equation with nonlocal integral conditions

Resumo

A variational method for the optimal control of moving sources governed by a parabolic equation with nonlocal integral conditions is considered. For this problem, an existence and uniqueness theorem is proved, necessary optimality conditions in the form of pointwise and integral maximum principles are obtained, sufficient conditions for the Fréchet differentiability of the cost functional are found, and an expression for its gradient is derived.