The Continuous Classical Optimal Control Problems for Triple Elliptic Partial Differential Equations

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J. A. Al-Hawasy Doaa Kateb Jasim

Abstract

In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

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How to Cite
AL-HAWASY, J. A.; JASIM, Doaa Kateb. The Continuous Classical Optimal Control Problems for Triple Elliptic Partial Differential Equations. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 33, n. 1, p. 143-151, jan. 2020. ISSN 2521-3407. Available at: <http://jih.uobaghdad.edu.iq/index.php/j/article/view/2380>. Date accessed: 25 may 2020. doi: http://dx.doi.org/10.30526/33.1.2380.
Section
mathematics