Identification of the Initial Temperature from the Given Temperature Data at the Left End of a Rod
Özet
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 (R) program.
Anahtar kelimeler
Atıf için künye
Akbulut, Y., & Şener Kılıç, S. Ş. (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
BibTeX
@article{akbulut2019-57458,
author = {Akbulut, Yeşim and Şener Kılıç, Sıdıka Şule},
title = {Identification of the Initial Temperature from the Given Temperature Data at the Left End of a Rod},
journal = {Applied Mathematics and Nonlinear Sciences},
year = {2019},
volume = {4},
number = {2},
pages = {469--474},
issn = {2444-8656},
doi = {10.2478/amns.2019.2.00044},
url = {https://akademik.atauni.edu.tr/yayinlar/57458-identification-of-the-initial-temperature-from-the-given-temperature-data-at-the}
}