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Solvability of Quaternary Mixed Optimal Control Governed by Elliptic System.

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Title: Solvability of Quaternary Mixed Optimal Control Governed by Elliptic System.
Authors: Jasim, Doaa K.1 (AUTHOR), Al-Hawasy, Jamil A. Ali2 (AUTHOR) jhawassy17@uomustansiriyah.edu.iq, Ali, Lamyaa H.2 (AUTHOR), Li, Feng (AUTHOR) fengli4131@ahut.edu.cn
Source: Journal of Applied Mathematics. 4/28/2026, Vol. 2026, p1-9. 9p.
Subjects: Optimal control theory, Elliptic equations, Adjoint differential equations, Galerkin methods, Operator functions, Uniqueness (Mathematics), Differential operators
Abstract: This paper studies the solvability of quaternary mixed optimal control problem (QMOCP) governed by the quaternary elliptic system (QES) in an infinite dimensional space. Under suitable hypotheses, the mathematical formulation of the weak form (WF) for the QES is found. Then, the proof of the existence of a unique QSSV of this WF is done by employing the Galerkin approach (GAP), when the quaternary mixed control vector (QMCV) is known. The Lipschitz operator (LO) from the control space into the state space is proved continuous. Under appropriate hypotheses, the existence of a QMOCV which is controlled by the WF of the QES is demonstrated. The mathematical formulation and the study of the quaternary adjoint equation (QAE) ruled by the QES are done. The Fréchet derivative (FD) for the cost function (CF) is determined, and the necessity for optimality of the MQOCP is proved. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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An: 193364669
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  Data: Solvability of Quaternary Mixed Optimal Control Governed by Elliptic System.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 4/28/2026, Vol. 2026, p1-9. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Optimal+control+theory%22">Optimal control theory</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+equations%22">Elliptic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Adjoint+differential+equations%22">Adjoint differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+functions%22">Operator functions</searchLink><br /><searchLink fieldCode="DE" term="%22Uniqueness+%28Mathematics%29%22">Uniqueness (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+operators%22">Differential operators</searchLink>
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  Label: Abstract
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  Data: This paper studies the solvability of quaternary mixed optimal control problem (QMOCP) governed by the quaternary elliptic system (QES) in an infinite dimensional space. Under suitable hypotheses, the mathematical formulation of the weak form (WF) for the QES is found. Then, the proof of the existence of a unique QSSV of this WF is done by employing the Galerkin approach (GAP), when the quaternary mixed control vector (QMCV) is known. The Lipschitz operator (LO) from the control space into the state space is proved continuous. Under appropriate hypotheses, the existence of a QMOCV which is controlled by the WF of the QES is demonstrated. The mathematical formulation and the study of the quaternary adjoint equation (QAE) ruled by the QES are done. The Fréchet derivative (FD) for the cost function (CF) is determined, and the necessity for optimality of the MQOCP is proved. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1155/jama/9871187
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      – Code: eng
        Text: English
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        PageCount: 9
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      – SubjectFull: Optimal control theory
        Type: general
      – SubjectFull: Elliptic equations
        Type: general
      – SubjectFull: Adjoint differential equations
        Type: general
      – SubjectFull: Galerkin methods
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      – SubjectFull: Operator functions
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      – SubjectFull: Uniqueness (Mathematics)
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      – SubjectFull: Differential operators
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      – TitleFull: Solvability of Quaternary Mixed Optimal Control Governed by Elliptic System.
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            NameFull: Jasim, Doaa K.
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            NameFull: Al-Hawasy, Jamil A. Ali
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            NameFull: Ali, Lamyaa H.
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            – D: 28
              M: 04
              Text: 4/28/2026
              Type: published
              Y: 2026
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