The Continuous Classical Boundary Optimal Control Vector Governing by Triple Linear Partial Differential Equations of Parabolic Type

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Jamil A. Al-Hawasy Mohammed A. K. Jaber

Abstract

In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and proved.

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How to Cite
AL-HAWASY, Jamil A.; K. JABER, Mohammed A.. The Continuous Classical Boundary Optimal Control Vector Governing by Triple Linear Partial Differential Equations of Parabolic Type. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 33, n. 3, p. 113-126, july 2020. ISSN 2521-3407. Available at: <http://jih.uobaghdad.edu.iq/index.php/j/article/view/2478>. Date accessed: 25 sep. 2020.
Section
mathematics