Optimal control problem for eliptic equation

In this thesis, an optimal control problem for the elliptic equation is discussed. In section 3.1 of this work, we first defined an optimal control problem for the elliptic equation. In section 3.2, the provision belonging to the existence and uniqueness of the generalized solutions, and the provision of it. Utilizing this provision, the problem of section 4.1 has been proved for solving of the optimal control problem and for the only expensive theorem. In section 4.2, objective functional were examined for differentiability and formula for gradient of functional were obtained. It was necessary and sufficient condition for the solution of optimal control problem. Finally, in section 4.3 of the work, an algorithm for solving of the optimal control problem is given.