Hào, DN, Thanh, PX, Lesnic, D et al. (1 more author) (2014) Determination of a source in the heat equation from integral observations. Journal of Computational and Applied Mathematics, 264. 82 - 98. ISSN 0377-0427
Abstract
A novel inverse problem which consists of the simultaneous determination of a source together with the temperature in the heat equation from integral observations is investigated. These integral observations are weighted averages of the temperature over the space domain and over the time interval. The heat source is sought in the form of a sum of two space- and time-dependent unknown components in order to ensure the uniqueness of a solution. The local existence and uniqueness of the solution in classical Hölder spaces are proved. The inverse problem is linear, but it is ill-posed because small errors in the input integral observations cause large errors in the output source. For a stable reconstruction a variational least-squares method with or without penalization is employed. The gradient of the functional which is minimized is calculated explicitly and the conjugate gradient method is applied. Numerical results obtained for several benchmark test examples show accurate and stable numerical reconstructions of the heat source.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2014, Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in the Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in the Journal of Computational and Applied Mathematics, 264, (2014). http://dx.doi.org/10.1016/j.cam.2014.01.005 |
Keywords: | Heat equation; Heat source; Conjugate gradient method; Inverse problem |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 Apr 2014 16:51 |
Last Modified: | 23 Jun 2023 21:39 |
Published Version: | http://dx.doi.org/10.1016/j.cam.2014.01.005 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.cam.2014.01.005 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:78512 |