Zhuo, L, Lesnic, D orcid.org/0000-0003-3025-2770, Ismailov, MI et al. (2 more authors) (2019) Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem. International Journal of Computer Mathematics, 96 (10). pp. 2079-2099. ISSN 0020-7160
Abstract
Diffusion processes with reaction generated by a nonlinear source are commonly encountered in practical applications related to ignition, pyrolysis and polymerization. In such processes, determining the intensity of reaction in time is of crucial importance for control and monitoring purposes. Therefore, this paper is devoted to such an identification problem of determining the time-dependent coefficient of a nonlinear heat source together with the unknown heat flux at an inaccessible boundary of a one-dimensional slab from temperature measurements at two sensor locations in the context of nonlinear transient heat conduction. Local existence and uniqueness results for the inverse coefficient problem are proved when the first three derivatives of the nonlinear source term are Lipschitz continuous functions. Furthermore, the conjugate gradient method (CGM) for separately reconstructing the reaction coefficient and the heat flux is developed. The ill-posedness is overcome by using the discrepancy principle to stop the iteration procedure of CGM when the input data is contaminated with noise. Numerical results show that the inverse solutions are accurate and stable.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Informa UK Limited, trading as Taylor and Francis Group. This is an author produced version of a paper published in the International Journal of Computer Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse heat source problem, inverse heat conduction problem, nonlinear source, conjugate gradient method, eigenfunction series expansion |
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: | 05 Dec 2018 12:00 |
Last Modified: | 05 Dec 2019 01:39 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/00207160.2018.1556790 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:139566 |