SOLVABILITY FOR CONTINUOUS CLASSICAL BOUNDARY OPTIMAL CONTROL OF COUPLE FOURTH ORDER LINEAR ELLIPTIC EQUATIONS
Keywords:
couple boundary optimal control, fourth order linear elliptic PDEs, variable coefficients, the corresponding couple adjoint equations.DOI:
https://doi.org/10.17654/0974324324012Abstract
In this paper, we study continuous classical boundary optimal control problem for the couple fourth order of linear elliptic system with variable coefficients. The existence theorem of a unique couple vector state solution of the weak form obtaining from the couple fourth order of linear elliptic system with Neumann conditions (NCs) is demonstrated for fixed continuous classical couple boundary control vector (CCCPBCTV) utilizing Hermite finite element method. The existence theorem of a couple continuous classical boundary optimal control vector dominated with the considered problem is proved. The existence and uniqueness of the solution of the couple adjoint equations (CPAEs) is discussed, when the classical couple optimal boundary control is given. Finally, the Fréchet derivative (FrD) of the Hamiltonian is obtained to establish the theorem of the necessary condition for optimality.
Received: January 27, 2024
Revised: April 22, 2024
Accepted: May 2, 2024
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