Cao, K. and Lesnic, D. orcid.org/0000-0003-3025-2770 (2024) Determination of the time-dependent effective ion collision frequency from an integral observation. Journal of Inverse and Ill-Posed Problems. ISSN 0928-0219
Abstract
Identification of physical properties of materials is very important because they are in general unknown. Furthermore, their direct experimental measurement could be costly and inaccurate. In such a situation, a cheap and efficient alternative is to mathematically formulate an inverse, but difficult, problem that can be solved, in general, numerically; the challenge being that the problem is, in general, nonlinear and ill-posed. In this paper, the reconstruction of a lower-order unknown time-dependent coefficient in a Cahn–Hilliard-type fourth-order equation from an additional integral observation, which has application to characterizing the nonlinear saturation of the collisional trapped-ion mode in a tokamak, is investigated. The local existence and uniqueness of the solution to such inverse problem is established by utilizing the Rothe method. Moreover, the continuous dependence of the unknown coefficient upon the measured data is derived. Next, the Tikhonov regularization method is applied to recover the unknown coefficient from noisy measurements. The stability estimate of the minimizer is derived by investigating an auxiliary linear fourth-order inverse source problem. Henceforth, the variational source condition can be verified. Then the convergence rate is obtained under such source condition.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article accepted for publication in Journal of Inverse and Ill-posed Problems, made available under the terms of the Creative Commons Attribution License (CC-BY), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Inverse problem; ill-posed problem; Rothe method; Tikhonov regularization method; Cahn–Hilliard 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: | 21 Nov 2023 11:28 |
Last Modified: | 07 Feb 2024 16:20 |
Status: | Published online |
Publisher: | De Gruyter |
Identification Number: | 10.1515/jiip-2023-0024 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:205577 |
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