In this study, the problem of determining the control function that is at the right hand side of a hyperbolic system from the final observation is investigated. Using the Fourier-Galerkin method, the weak solution of this hyperbolic system is obtained. The necessary conditions for the existence and uniqueness of the optimal solution are proved. We also find the approximate solutions of the test problems in numerical examples by a MAPLE® program. Finally, the numerical results are presented in the form of tables.
| Published in | Applied and Computational Mathematics (Volume 7, Issue 3) |
| DOI | 10.11648/j.acm.20180703.11 |
| Page(s) | 75-82 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2018. Published by Science Publishing Group |
Optimal Control, Partial Differential Equation, Numerical Approximation
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APA Style
Fatma Toyoğlu. (2018). On the Solution of a Optimal Control Problem for a Hyperbolic System. Applied and Computational Mathematics, 7(3), 75-82. https://doi.org/10.11648/j.acm.20180703.11
ACS Style
Fatma Toyoğlu. On the Solution of a Optimal Control Problem for a Hyperbolic System. Appl. Comput. Math. 2018, 7(3), 75-82. doi: 10.11648/j.acm.20180703.11
AMA Style
Fatma Toyoğlu. On the Solution of a Optimal Control Problem for a Hyperbolic System. Appl Comput Math. 2018;7(3):75-82. doi: 10.11648/j.acm.20180703.11
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Download@article{10.11648/j.acm.20180703.11,
author = {Fatma Toyoğlu},
title = {On the Solution of a Optimal Control Problem for a Hyperbolic System},
journal = {Applied and Computational Mathematics},
volume = {7},
number = {3},
pages = {75-82},
doi = {10.11648/j.acm.20180703.11},
url = {https://doi.org/10.11648/j.acm.20180703.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180703.11},
abstract = {In this study, the problem of determining the control function that is at the right hand side of a hyperbolic system from the final observation is investigated. Using the Fourier-Galerkin method, the weak solution of this hyperbolic system is obtained. The necessary conditions for the existence and uniqueness of the optimal solution are proved. We also find the approximate solutions of the test problems in numerical examples by a MAPLE® program. Finally, the numerical results are presented in the form of tables.},
year = {2018}
}
TY - JOUR T1 - On the Solution of a Optimal Control Problem for a Hyperbolic System AU - Fatma Toyoğlu Y1 - 2018/05/25 PY - 2018 N1 - https://doi.org/10.11648/j.acm.20180703.11 DO - 10.11648/j.acm.20180703.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 75 EP - 82 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20180703.11 AB - In this study, the problem of determining the control function that is at the right hand side of a hyperbolic system from the final observation is investigated. Using the Fourier-Galerkin method, the weak solution of this hyperbolic system is obtained. The necessary conditions for the existence and uniqueness of the optimal solution are proved. We also find the approximate solutions of the test problems in numerical examples by a MAPLE® program. Finally, the numerical results are presented in the form of tables. VL - 7 IS - 3 ER -
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