Identification of the Initial Temperature from the Given Temperature Data at the Left End of a Rod

Saraç Y., Şener Kılıç S. Ş.

Applied Mathematics and Nonlinear Sciences, cilt.4, sa.2, ss.469-474, 2019 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2478/amns.2019.2.00044
  • Dergi Adı: Applied Mathematics and Nonlinear Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Applied Science & Technology Source, Compendex, zbMATH, DIALNET
  • Sayfa Sayıları: ss.469-474
  • Anahtar Kelimeler: Optimal Control, Frechet Differential, Adjoint Approach
  • Atatürk Üniversitesi Adresli: Evet

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.