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

Year 2024, Volume: 25 Issue: 2, 289 - 299, 28.06.2024
https://doi.org/10.18038/estubtda.1479718

Abstract

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.

Ethical Statement

The author declares no conflicts of interest.

Supporting Institution

Not applicable.

References

  • [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

Year 2024, Volume: 25 Issue: 2, 289 - 299, 28.06.2024
https://doi.org/10.18038/estubtda.1479718

Abstract

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.

References

  • [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
There are 12 citations in total.

Details

Primary Language English
Subjects Numerical Solution of Differential and Integral Equations, Mathematical Optimisation, Applied Mathematics (Other)
Journal Section Articles
Authors

Hakkı Güngör 0000-0002-9546-665X

Publication Date June 28, 2024
Submission Date May 7, 2024
Acceptance Date June 22, 2024
Published in Issue Year 2024 Volume: 25 Issue: 2

Cite

AMA Güngör H. ON THE CONTROL AND SIMULATION OF THE THERMAL CONDUCTIVITY IN A HEAT EQUATION. Estuscience - Se. June 2024;25(2):289-299. doi:10.18038/estubtda.1479718