The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem
This work is concerned with studying the optimal classical continuous control quaternary vector problem. It is consisted of; the quaternary nonlinear hyperbolic boundary value problem and the cost functional. At first, the weak form of the quaternary nonlinear hyperbolic boundary value problem is o...
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| Format: | Article |
| Language: | English |
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University of Baghdad
2022-07-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/2833 |
| _version_ | 1811215046773047296 |
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| author | jamil Amir Al-Hawasy Mayeada Abd Alsatar Hassan |
| author_facet | jamil Amir Al-Hawasy Mayeada Abd Alsatar Hassan |
| author_sort | jamil Amir Al-Hawasy |
| collection | DOAJ |
| description |
This work is concerned with studying the optimal classical continuous control quaternary vector problem. It is consisted of; the quaternary nonlinear hyperbolic boundary value problem and the cost functional. At first, the weak form of the quaternary nonlinear hyperbolic boundary value problem is obtained. Then under suitable hypotheses, the existence theorem of a unique state quaternary vector solution for the weak form where the classical continuous control quaternary vector is considered known is stated and demonstrated by employing the method of Galerkin and the compactness theorem. In addition, the continuity operator between the state quaternary vector solution of the weak form and the corresponding classical continuous control quaternary vector is demonstrated in three different infinite dimensional spaces (Hilbert spaces). Furthermore, with suitable hypotheses, the existence theorem of an optimal classical continuous control quaternary vector dominated by the weak form of the quaternary nonlinear hyperbolic boundary value problem is stated and demonstrated.
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| first_indexed | 2024-04-12T06:14:48Z |
| format | Article |
| id | doaj.art-4b8e32e267b04fe89858e787fec61137 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-04-12T06:14:48Z |
| publishDate | 2022-07-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-4b8e32e267b04fe89858e787fec611372022-12-22T03:44:31ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072022-07-0135310.30526/35.3.2833The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problemjamil Amir Al-Hawasy0Mayeada Abd Alsatar Hassan1Department of Mathematics, College of Sciences, Mustansiriyah University, Baghdad, IraqBaghdad Directorate of Education, Baghdad, Iraq This work is concerned with studying the optimal classical continuous control quaternary vector problem. It is consisted of; the quaternary nonlinear hyperbolic boundary value problem and the cost functional. At first, the weak form of the quaternary nonlinear hyperbolic boundary value problem is obtained. Then under suitable hypotheses, the existence theorem of a unique state quaternary vector solution for the weak form where the classical continuous control quaternary vector is considered known is stated and demonstrated by employing the method of Galerkin and the compactness theorem. In addition, the continuity operator between the state quaternary vector solution of the weak form and the corresponding classical continuous control quaternary vector is demonstrated in three different infinite dimensional spaces (Hilbert spaces). Furthermore, with suitable hypotheses, the existence theorem of an optimal classical continuous control quaternary vector dominated by the weak form of the quaternary nonlinear hyperbolic boundary value problem is stated and demonstrated. https://jih.uobaghdad.edu.iq/index.php/j/article/view/2833 |
| spellingShingle | jamil Amir Al-Hawasy Mayeada Abd Alsatar Hassan The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem Ibn Al-Haitham Journal for Pure and Applied Sciences |
| title | The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem |
| title_full | The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem |
| title_fullStr | The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem |
| title_full_unstemmed | The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem |
| title_short | The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem |
| title_sort | optimal classical continuous control quaternary vector of quaternary nonlinear hyperbolic boundary value problem |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/2833 |
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