An inverse problem in estimating the time dependent source term and initial temperature simultaneously by the polynomial regression and conjugate gradient method

2020/06/10 by Arzu Erdem Coşkun, Coşkun, Arzu Erdem
Mathematics · #Analysis of PDEs (math.AP) #F.2.1 #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2006.08366

13 pages and 6 figures

arxiv created 2020/06/10 · arxiv updated 2020/06/16

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 the evolutionary algorithm are presented for various test examples.

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