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# Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

IMPACT FACTOR 2017: 0.941
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CiteScore 2017: 0.91

SCImago Journal Rank (SJR) 2017: 0.461
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ISSN
1569-3945
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# An adaptive algorithm for determination of source terms in a linear parabolic problem

Arzu Erdem
• Department of Mathematics, Faculty of Arts and Sciences, Kocaeli University, Umuttepe Campus, 41380, Kocaeli, Turkey
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Published Online: 2013-12-07 | DOI: https://doi.org/10.1515/jip-2013-0019

## Abstract

This paper investigates an adaptive algorithm for identification of source terms $w:=\left\{F\left(x,t\right);p\left(t\right)\right\}$ in the linear parabolic equation ${u}_{t}={u}_{xx}+F\left(x,t\right)$ and Robin boundary condition $-{u}_{x}\left(l,t\right)=\nu \left[u\left(l,t\right)-p\left(t\right)\right]$ 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.

MSC: 35R30; 46N10; 49N50

Published Online: 2013-12-07

Published in Print: 2014-08-01

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 22, Issue 4, Pages 569–592, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219,

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