An adaptive algorithm for determination of source terms in a linear parabolic problem

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Erdem A.

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, vol.22, no.4, pp.569-592, 2014 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 22 Issue: 4
• Publication Date: 2014
• Doi Number: 10.1515/jip-2013-0019
• Journal Name: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.569-592
• Kocaeli University Affiliated: Yes

Abstract

This paper investigates an adaptive algorithm for identification of source terms w := {F (x, t); p (t)} in the linear parabolic equation u(t) = u(xx) + F (x, t) and Robin boundary condition -u(x) (l, t) = nu[u (l, t) - p (t)] from the measured final data and the measurement of the temperature in a subregion. This is based on the minimization of Tikhonov functional. We pursue the approach iteratively regularized gradient method. Results with the adaptive algorithm are presented.