An Inverse Problem in Estimating the Time Dependent Source Term and Initial Temperature Simultaneously by the Polynomial Regression and Conjugate Gradient Method

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Coskun A.

FILOMAT, vol.34, no.10, pp.3507-3516, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 10
  • Publication Date: 2020
  • Doi Number: 10.2298/fil2010507c
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.3507-3516
  • Keywords: Inverse source problem, parabolic problem, Tikhonov functional, polynomial regression, conjugate gradient method, RIGHT-HAND SIDE, NUMERICAL-METHOD, EQUATION, IDENTIFICATION
  • Kocaeli University Affiliated: Yes

Abstract

From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be effective in dealing with these problems. However, they require to find the gradient information. This idea has been employed in this research. We derive the gradient of Tikhonov functional and establish the stability of the minimizer from the necessary condition. The stability and effectiveness of evolutionary algorithm are presented for various test examples.