Quaternary Continuous Classical Boundary Optimal Control Problem Dominating by Parabolic System

Authors

  • Fetan J. Naji Department of Mathematics, College of Science, Mustansiriyah University, Iraq, Baghdad
  • Jamil A. Ali Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Iraq, Baghdad https://orcid.org/0000-0002-7225-8030

DOI:

https://doi.org/10.24996/ijs.2024.65.3.26

Keywords:

Quaternary continuous classical boundary optimal control vector problem, Quaternary linear parabolic boundary value problem, Method of Galerkin, Lipschitz continuity operator

Abstract

     In this paper, our purpose is to study the quaternary continuous classical boundary optimal control vector problem dominated by a quaternary linear parabolic boundary value problem. Under suitable assumptions and with a given quaternary continuous classical boundary control vector, the existence theorem for a unique quaternary state vector solution to the weak form is stated and demonstrated via the method of Galerkin. Furthermore, the continuity of the Lipschitz operator between the state vector solution to the weak form for the dominating equations and the corresponding are proved. The existence of a quaternary continuous classical boundary optimal control vector is stated and demonstrated under suitable Assumptions. The mathematical formulation for the quaternary adjoint boundary value problem associated with each considered boundary value problem is obtained and the Frѐchet derivative for the objective function is derived. Finally, the necessary conditions for the optimality theorem of the problem are stated and demonstrated.

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Published

2024-03-29

Issue

Section

Mathematics

How to Cite

Quaternary Continuous Classical Boundary Optimal Control Problem Dominating by Parabolic System. (2024). Iraqi Journal of Science, 65(3), 1485-1501. https://doi.org/10.24996/ijs.2024.65.3.26

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