Hussein, MS, Lesnic, D orcid.org/0000-0003-3025-2770, Kamynin, VL et al. (1 more author) (2020) Direct and inverse source problems for degenerate parabolic equations. Journal of Inverse and Ill-Posed Problems, 28 (3). pp. 425-448. ISSN 0928-0219
Abstract
Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Walter de Gruyter GmbH, Berlin/Boston. This is an author produced version of an article published in Journal of Inverse and Ill-posed Problems. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse source problem; degenerate parabolic equation; integral observation; 35K20; 35R30 |
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: | 06 Feb 2020 11:26 |
Last Modified: | 10 Mar 2021 01:38 |
Status: | Published |
Publisher: | De Gruyter |
Identification Number: | 10.1515/jiip-2019-0046 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:156370 |