Cao, K, Lesnic, D orcid.org/0000-0003-3025-2770 and Ismailov, MI (2021) Determination of the time-dependent thermal grooving coefficient. Journal of Applied Mathematics and Computing, 65 (1-2). pp. 199-221. ISSN 1598-5865
Abstract
Changes in morphology of a polycrystalline material may occur through interface motion under the action of a driving force. An important special case that is considered in this paper is the thermal grooving that occurs when a grain boundary intersects the flat surface of a recently solidified metal slab giving rise to the formation of a thin symmetric groove. In case the transient surface diffusion is the main forming mechanism this yields a fourth-order time-dependent partial differential equation with unknown time-dependent surface diffusivity. In order to determine it, the profile of the free grooving surface at a fixed location is recorded in time. The grooving boundaries are supported by self-adjoint boundary conditions. We provide sufficient conditions on the input data for which the resulting coefficient identification problem is proved to be well-posed. Furthermore, we develop a predictor–corrector finitedifference spline method for obtaining an accurate and stable numerical solution to the nonlinear coefficient identification problem. Numerical results illustrate the performance of the inversion of both exact and noisy data.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Korean Society for Informatics and Computational Applied Mathematics 2020. This is an author produced version of a paper published in Journal of Applied Mathematics and Computing. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse problems · Fourth-order parabolic equation · Thermal grooving coefficient · Predictor–corrector method |
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: | 23 Jun 2020 11:27 |
Last Modified: | 27 Jun 2022 10:31 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s12190-020-01388-7 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:162209 |