TY - JOUR ID - TI - The Continuous Classical Boundary Optimal Control Vector Governing by Triple Linear Partial Differential Equations of Parabolic Type AU - Jamil A. Al-Hawasy AU - Mohammed A. K. Jaber PY - 2020 VL - 33 IS - 3 SP - 113 EP - 126 JO - Ibn Al-Haitham Journal For Pure and Applied Sciences مجلة ابن الهيثم للعلوم الصرفة والتطبيقية SN - 16094042 25213407 AB - 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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