Hazanee, A, Lesnic, D, Ismailov, MI et al. (1 more author) (2015) An inverse time-dependent source problem for the heat equation with a non-classical boundary condition. Applied Mathematical Modelling, 39 (20). 6258 - 6272. ISSN 0307-904X
Abstract
This paper investigates the inverse problem of determining the time-dependent heat source and the temperature for the heat equation with a non-classical boundary and an integral over-determination conditions. The existence, uniqueness and continuous dependence upon the data of the classical solution of the inverse problem is shown by using the generalised Fourier method. Furthermore in the numerical process, the boundary element method (BEM) together with the second-order Tikhonov regularization is employed with the choice of regularization parameter based on the generalised cross-validation (GCV) criterion. Numerical results are presented and discussed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2015 Elsevier Inc. This is an author produced version of a paper published in Applied Mathematical Modelling. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Heat equation; Inverse source problem; Non-classical boundary conditions; Generalised Fourier 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: | 14 Jul 2015 13:22 |
Last Modified: | 16 Nov 2016 12:32 |
Published Version: | http://dx.doi.org/10.1016/j.apm.2015.01.058 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.apm.2015.01.058 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:84757 |