Eman Hussain Mukhalf Al-Rawdhanee

SOLVABILITY FOR CONTINUOUS CLASSICAL BOUNDARY OPTIMAL CONTROL OF COUPLE FOURTH ORDER LINEAR ELLIPTIC EQUATIONS

Introduction

Solvability for continuous classical boundary optimal control of couple fourth order linear elliptic equations. Studies solvability for continuous boundary optimal control of coupled fourth-order linear elliptic systems. Proves existence/uniqueness via Hermite FEM, adjoint equations, and Fréchet derivative.

Abstract

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, 2024Revised: April 22, 2024Accepted: May 2, 2024

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