Adil, Z, Hussein, MS and Lesnic, D orcid.org/0000-0003-3025-2770 (2021) Determination of time-dependent coefficients in moving boundary problems under nonlocal and heat moment observations. International Journal of Computational Engineering Science, 22 (6). pp. 500-513. ISSN 1550-2287
Abstract
This paper investigates the reconstruction of time-dependent coefficients in the transient heat equation in a moving boundary domain with unknown free boundaries. This problem is considered under Stefan/heat moments overdetermination conditions also dependent of time. This inverse problem is nonlinear. Moreover, although local existence and uniqueness of solution hold, the problem is still ill-posed since small errors into the input data lead to large errors in the reconstructed coefficients. In order to obtain a stable solution, the nonlinear Tikhonov regularization method is employed. This recasts as minimizing a regularization functional subject to simple bounds on variables. Numerically, this is accomplished using the Matlab toolbox optimization routine lsqnonlin. Numerical results illustrate that stable and accurate solutions are obtained.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Taylor & Francis Group, LLC. This is an author produced version of an article published in International Journal for Computational Methods in Engineering Science and Mechanics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Moving boundary problem, inverse problem, coefficient identification problem, nonlinear optimization, reaction-diffusion, equation |
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: | 17 Feb 2021 15:58 |
Last Modified: | 16 Mar 2022 01:38 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/15502287.2021.1892870 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:171263 |