PUBLISHED PAPERS #04.10
| Rafig Taghiyev, Aitaj Mammadova. An Optimal Control Problem for an Elliptic Equation |
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| Abstract. An optimal control problem for an elliptic equation with periodic boundary condition is considered. The correctness of the problem statement is investigated. The existence and uniqueness of the generalized solution to the boundary problem for the fixed controls is proved and a priori estimation for its solution is obtained. The theorem on the existence and uniqueness of the solution to the considered optimal control problem is proved. It is proved that the objective functional is differentiable on the space of controls, and an explicit expression for its gradient is derived. Necessary and sufficient conditions for the optimality of the controls are obtained. |
| Keywords: elliptic equation, optimal control, periodicity conditions, correctness of problem statement, optimality criterion |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.1056 |