Quaternary Boundary Optimal Control Problem Dominating by Quaternary Nonlinear Parabolic System
Keywords:Quaternary continuous classical boundary optimal control vector problem, Quaternary nonlinear parabolic boundary value problem, Method of Galerkin, Lipschitz continuity
In this paper, our purpose is to study the quaternary continuous classical boundary optimal control vector problem (QCCBOCVP) dominated by the quaternary nonlinear parabolic boundary value problem (QNLPBVP). Under suitable assumptions and with given quaternary continuous classical boundary control vector (QCCBCV), the existence theorem for a unique quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVP is stated and demonstrated via the Method of Galerkin and the first compactness theorem. Furthermore, the continuity of the Lipchitz operator between the QSVS of the WF for the QLPBVP and the corresponding QCCBCV is proved. The existence of a quaternary continuous classical boundary optimal control vector (QCCBOVC) is stated and demonstrated under suitable assumptions.
M.G. Cojocaru, A.S. Jaber, " Optimal Control of a Vaccinating Game Toward Increasing Overall Coverage," J. appl. Math. Phys., Vol.6, 2018, pp. 754-769.
E. Staffetti E, X. Li, Y. Matsuno, M. Soler, "Optimal Control Techniques in Aircraft Guidance and Control,," Int. J. Aerosp. Eng., 2019, 2 pages.
I. Syahrini, R. Masabar, A. Aliasuddin, S. Munzir, Y. Hazim, "The Application of Optimal Control Through Fiscal Policy on Indonesian Economy," J. Asian Finance Econ. Bus. Vol.8, No. 3, 2021, pp. 0741-0750.
G. Rigatos, M. Abbaszadeh, "Nonlinear Optimal Control for Multi-DOF Robotic Manipulators with Flexible Joints," Optim. Control Appl. Methods, Vol.42, No. 6,2021, pp. 1708-1733.
D. Derome D, H. Razali, A. Fazlizan, A. Jedi, K.P. Roberts. Determination of Optimal Time -Average Wind Speed Data in the Southern Part of Malaysia. Baghdad Sci. J. Vol.19, No.5,2022, pp.1111-1122.
P. Lin, W. Wang, "Optimal Control Problems for Some Ordinary Differential Equations with Behavior of Blowup or Quenching," Math. Control Relat. Fields.Vol.8, No. 4, 2018, pp. 809-828.
A. Manzoni, A. Quarteroni, S. Salsa, Optimal Control of Partial Differential Equations: Analysis, Approximation, and Applications (Applied Mathematical Sciences, 207). 1st edition. New York: Spriger;2021, p. 515.
J. A. Ali Al-Hawasy, A. A. H. Naeif, "The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Parabolic Partial Differential Equations," Special Issus: 1st Scientific International Conference, College of Science, Al-Nahrain University, Part I, pp.123-136, 21-22/11/2017.
J. A. Ali Al-Hawasy, S. J. M. Al-Qaisi," The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Elliptic Partial Differential Equations with State Constraints," Al-Mustansiriyah J. of Sci. Vol. 30, Issue 1,2019, pp.143-151.
J. A. Ali Al-Hawasy, "The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints," Baghdad Sci. J.Vol.16, No.4, Supplement 2019, pp.1064-1074.
J. A. Ali Al-Hawasy, Yasameen H. Rashid," Classical Continuous Boundary Optimal Control Vector Problem for Triple Nonlinear Parabolic System," Al-Mustansiriyah J. of Sci., Accepted for publishing in Vol. 34, No.1, 2023.
J. A. A. Al-Hawas, N. A. Th. Al-Ajeeli, "The Continuous Classical Boundary Optimal Control of Triple Nonlinear Elliptic Partial Differential Equations with State Constraints," Iraqi J. of Sci., Vol.62, No.9, 2021,pp.3020-3030.
L. H Ali J. A. Al-Hawasy," Boundary Optimal Control for Triple Nonlinear Hyperbolic Boundary Value Problem with State Constraints," Iraqi J. of Sci., Vol 62, No 6, 2021, pp.2009-2021.
R. Temam, Navier-Stokes equations. Amsterdam-New York: North-Holand Publishing Company; 1977.
How to Cite
Copyright (c) 2023 Al-Mustansiriyah Journal of Science
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.