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ON THE CONTROL AND SIMULATION OF THE THERMAL CONDUCTIVITY IN A HEAT EQUATION

Yıl 2024, , 289 - 299, 28.06.2024
https://doi.org/10.18038/estubtda.1479718

Öz

This study operates the Gradient Method to control the leading coefficient function of a heat equation and presents a Maplet Application which facilitates the computation of control function. The control is heat conductivity function and this function is controlled by aiming the desired value approximation of final heat. After mentioning the existence and uniqueness of the control, the application is submitted by MAPLE mathematical software program and the results are tested on a problem.

Etik Beyan

The author declares no conflicts of interest.

Destekleyen Kurum

Not applicable.

Kaynakça

  • [1] Subaşı M. Optimal Control of Heat Source in a Heat Conductivity Problem. Optimization Methods and Software, 2002; 17, 239-250
  • [2] Effati S, Nazemi A, Shabani H. Time Optimal Control Problem of the Heat Equation with Thermal Source, IMA Journal of Mathematical Control and Information, Volume 31, 2014; pp. 384-402
  • [3] Teymurov R. Optimal control of mobile sources for heat conductivity processes, International Journal of Control, Volume 90, Issue 5, 2017; pp. 923-931
  • [4] Tagiyev R. Optimal Coefficient Control in Parabolic Systems, Differential Equations, Volume 45, no. 10, 2009; pp. 1526-1535
  • [5] Tagiyev R. Optimal control for the coefficients of a Quasilinear parabolic equation, Automation and Remote Control, volume 70, no. 11, 2009; pp. 1814-1826
  • [6] Tagiyev R. Optimal control problem for a Quasilinear parabolic equation with Controls in the coefficients and with State Constraints, Differential Equations, Volume 49, no. 3, 2013; pp. 369-381
  • [7] Tagiyev RK. Hashimov SA. On Optimal Control of the coefficients of a parabolic equation Involving Phase Constraints, Proceedings of IMM of National Academy of Sciences of Azerbaijan, volume 38 , 2013; pp. 131-146
  • [8] Engl HW, Hanke M, Neubauer A. Regularization of Inverse Problems. Kluwer Academic Publishers, Dordrecht, 1996.
  • [9] Goebel M. On existence of optimal control. Math.Nachrichten, 93, 1979; pp. 67–73
  • [10] https://www.maplesoft.com/support/help/maple/view.aspx?path=MapletsOverview, Date of Access: 2023.
  • [11] Vasilyev FP. Numerical Methods for Solving Extremal Problems. Nauka, 400 s, Moscow, 1981.
  • [12] https://drive.google.com/file/d/1dhlFVmxwnD2km3xyDut0098YPUKfc4j8/view?usp=sharing

ON THE CONTROL AND SIMULATION OF THE THERMAL CONDUCTIVITY IN A HEAT EQUATION

Yıl 2024, , 289 - 299, 28.06.2024
https://doi.org/10.18038/estubtda.1479718

Öz

This study operates the Gradient Method to control the leading coefficient function of a heat equation and presents a Maplet Application which facilitates the computation of control function. The control is heat conductivity function and this function is controlled by aiming the desired value approximation of final heat. After mentioning the existence and uniqueness of the control, the application is submitted by MAPLE mathematical software program and the results are tested on a problem.

Kaynakça

  • [1] Subaşı M. Optimal Control of Heat Source in a Heat Conductivity Problem. Optimization Methods and Software, 2002; 17, 239-250
  • [2] Effati S, Nazemi A, Shabani H. Time Optimal Control Problem of the Heat Equation with Thermal Source, IMA Journal of Mathematical Control and Information, Volume 31, 2014; pp. 384-402
  • [3] Teymurov R. Optimal control of mobile sources for heat conductivity processes, International Journal of Control, Volume 90, Issue 5, 2017; pp. 923-931
  • [4] Tagiyev R. Optimal Coefficient Control in Parabolic Systems, Differential Equations, Volume 45, no. 10, 2009; pp. 1526-1535
  • [5] Tagiyev R. Optimal control for the coefficients of a Quasilinear parabolic equation, Automation and Remote Control, volume 70, no. 11, 2009; pp. 1814-1826
  • [6] Tagiyev R. Optimal control problem for a Quasilinear parabolic equation with Controls in the coefficients and with State Constraints, Differential Equations, Volume 49, no. 3, 2013; pp. 369-381
  • [7] Tagiyev RK. Hashimov SA. On Optimal Control of the coefficients of a parabolic equation Involving Phase Constraints, Proceedings of IMM of National Academy of Sciences of Azerbaijan, volume 38 , 2013; pp. 131-146
  • [8] Engl HW, Hanke M, Neubauer A. Regularization of Inverse Problems. Kluwer Academic Publishers, Dordrecht, 1996.
  • [9] Goebel M. On existence of optimal control. Math.Nachrichten, 93, 1979; pp. 67–73
  • [10] https://www.maplesoft.com/support/help/maple/view.aspx?path=MapletsOverview, Date of Access: 2023.
  • [11] Vasilyev FP. Numerical Methods for Solving Extremal Problems. Nauka, 400 s, Moscow, 1981.
  • [12] https://drive.google.com/file/d/1dhlFVmxwnD2km3xyDut0098YPUKfc4j8/view?usp=sharing
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Diferansiyel ve İntegral Denklemlerin Sayısal Çözümü, Matematikte Optimizasyon, Uygulamalı Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Hakkı Güngör 0000-0002-9546-665X

Yayımlanma Tarihi 28 Haziran 2024
Gönderilme Tarihi 7 Mayıs 2024
Kabul Tarihi 22 Haziran 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

AMA Güngör H. ON THE CONTROL AND SIMULATION OF THE THERMAL CONDUCTIVITY IN A HEAT EQUATION. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering. Haziran 2024;25(2):289-299. doi:10.18038/estubtda.1479718