Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 4, Issue 2


Published
on

December 18, 2019


Pages

469-474


DOI

Article

Identification of the initial temperature from the given temperature data at the left end of a rod

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Authors

Yesim Sarac Affiliation:
Ataturk University, Science Faculty, Department of Mathematics, 25240, Erzurum, Turkey
and S. Sule Sener Affiliation:
Ataturk University, Science Faculty, Department of Mathematics, 25240, Erzurum, Turkey


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

Published by: Engineering Journals

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