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Article
The Continuous Classical Optimal Control for a Coupled Nonlinear Parabolic Partial Differential Equations with Equality and Inequality Constraints

Authors: Jamil A. Ali Al-Hawasy --- Ghufran M. Kadhem
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2016 Volume: 19 Issue: 1 Pages: 173-186
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

This paper is concerned with the existence and uniqueness state vector solution for a coupled of nonlinear parabolic equations using the Galerkin method when the continuous classical control vector is given, the existence theorem of a continuous classical optimal control vector with equality and inequality vector state constraints is proved, the existence and uniqueness solution of the adjoint equations associated with the state equations is studied. The derivation of the Frcéhet derivative of the Hamiltonian is obtained. Finally the necessary conditions theorem, so as the sufficient conditions theorem of optimality of the constrained problem are proved.

يهتم هذا البحث بمسألة وجود ووحدانية حل لزوج من المعادلات التفاضلية من النوع المكافئ باستخدام طريقة كاليركن عندما يكون متجه السيطرة التقليدية "Classical control vector" ثابتا". يتناول ايضا" برهان لمبرهنة وجود سيطرة امثلية مستمرة تقليدية بوجود قيدي التساوي وعدم التساوي. كذلك برهان مبرهنة وجود حل لزوج من المعادلات الملحقة "Adjoint equations" لمعادلات الحالة. تم اشتقاق مشتقة فريشيه "Frcéhet" لدالة هاملتون الخاصة بهذه المسالة. ايضا تم برهان مبرهنتا الشروط الضرورية والكافية لوجود متجه سيطرة امثلية مستمرة تقليدية بوجود قيدي التساوي وعدم التساوي.


Article
The Continuous Classical Optimal Boundary Control of a Couple Linear Elliptic Partial Differential Equations

Authors: Safaa J. Mohammed Al-Qaisi --- Jamil A. Ali Al-Hawasy
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2018 Volume: 00 Issue: 1 Pages: 137-142
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

This paper is concerned with the proof of the existence and uniqueness theorem for the solution of the state vector of a couple linear elliptic partial differential equations using the Galerkin method, where the continuous classical boundary control vector is given. Also, the existence theorem of a continuous classical boundary optimal control vector governed by the couple of linear elliptic partial differential equation is proved. The existence and the uniqueness solution of the couple of adjoint equations associated with the considered couple of the state equations studied. The derivation of the Fréchet derivative of the Hamiltonian is developed. The necessary conditions theorem of optimality of this problem is proved.

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