research centers


Search results: Found 2

Listing 1 - 2 of 2
Sort by

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

Loading...
Loading...
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.


Article
The Solvability of the Continuous Classical Boundary Optimal Control of Couple Nonlinear Elliptic Partial Differential Equations with State Constraints

Authors: Jamil A. Ali Al-Hawasy --- Safaa J. Mohammed Al-Qaisi
Journal: Al-Mustansiriyah Journal of Science مجلة علوم المستنصرية ISSN: 1814635X Year: 2019 Volume: 30 Issue: 1 Pages: 143-151
Publisher: Al-Mustansyriah University الجامعة المستنصرية

Loading...
Loading...
Abstract

This paper concerns with, the proof of the existence and the uniqueness theorem for the solution of the state vector of couple of nonlinear elliptic partial differential equations by using the Minty-Browder theorem, where the continuous classical boundary control vector is given. Also the existence theorem of a continuous classical boundary optimal control vector governing by the couple of nonlinear elliptic partial differential equation with equality and inequality constraints is proved. The existence of the uniqueness solution of the couple of adjoin equations which is associated with the couple of the state equations with equality and inequality constraints is studied. The necessary and sufficient conditions theorem for optimality of the couple of nonlinear elliptic equations with equality and inequality constraints are proved by using the Kuhn-Tucker-Lagrange multipliers theorems.

يتناول هذا البحث مبرهنة وجود وحدانية الحل لمتجه الحالة لزوج من المعادلات التفاضلية الجزئية الغير خطية من النمط الاهليجي باستخدام مبرهنة مينتي- براودر عندما يكون متجه السيطرة الحدودية التقليدية المستمرة ثابتا". ايضا يتناول مبرهنة الوجود لمتجه سيطرة امثلية حدودية مستمرة تقليدية المسيطر بواسطة الزوجان من المعادلة التفاضلية الجزئية الغير خطية بوجود قيدي التساوي والتباين. تمت دراسة مسالة وجود وحدانية الحل للمعادلة المرافقة لزوج المعادلات التفاضلية الجزئية الغير خطية من النمط الاهليجي بوجود قيدي التساوي والتباين. استخدمت مبرهنتي كان-تاكر-لاكرانج لبرهان مبرهنتي الشرط الضروري والكافي لوجود السيطرة الأمثلية الحدودية التقليدية المستمرة بوجود قيدي التساوي والتباين.

Listing 1 - 2 of 2
Sort by
Narrow your search

Resource type

article (2)


Language

English (2)


Year
From To Submit

2019 (1)

2018 (1)