Article
Identification of the initial temperature from the given temperature data at the left end of a rod
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Abstract
This study aims to investigate the problem of determining the unknown initial temperature in a variable coefficient heat equation. We obtain the existence and uniqueness of the solution of the optimal control problem considered under some conditions. Using the adjoint problem approach, we get the Frechet differential of the cost functional. We construct a minimizing sequence and give the convergence rate of this sequence. Also, we test the theoretical results in a numerical example by using the MAPLE® program.
Keywords
Optimal Control, Frechet Differential, Adjoint Approach, 49J20, 49J50
Citation
Sarac, Y. & Sener, S. S. (2019). Identification of the initial temperature from the given temperature data at the left end of a rod. Applied Mathematics and Nonlinear Sciences, 4(2), 469–474. https://doi.org/10.2478/AMNS.2019.2.00044
Y. Sarac and S. S. Sener, “Identification of the initial temperature from the given temperature data at the left end of a rod,” Applied Mathematics and Nonlinear Sciences, vol. 4, no. 2, pp. 469–474, 2019, doi: 10.2478/AMNS.2019.2.00044.
Sarac Y, Sener SS. Identification of the initial temperature from the given temperature data at the left end of a rod. Applied Mathematics and Nonlinear Sciences. 2019;4(2):469–474. doi:10.2478/AMNS.2019.2.00044.
Sarac, Y. and Sener, S. S. (2019), ‘Identification of the initial temperature from the given temperature data at the left end of a rod’, Applied Mathematics and Nonlinear Sciences, 4(2), pp. 469–474. Available at: https://doi.org/10.2478/AMNS.2019.2.00044.
Sarac, Yesim, and S. Sule Sener. “Identification of the Initial Temperature from the Given Temperature Data at the Left End of a Rod.” Applied Mathematics and Nonlinear Sciences, vol. 4, no. 2, 2019, pp. 469–474. https://doi.org/10.2478/AMNS.2019.2.00044.
Sarac, Yesim, and S. Sule Sener. “Identification of the Initial Temperature from the Given Temperature Data at the Left End of a Rod.” Applied Mathematics and Nonlinear Sciences 4, no. 2 (2019): 469–474. https://doi.org/10.2478/AMNS.2019.2.00044.
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