Huy Tuan, N, Van Au, V, Anh Khoa, V et al. (1 more author) (2017) Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction. Inverse Problems, 33 (5). 055019. ISSN 0266-5611
Abstract
The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L²-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record will be available online at https://doi.org/10.1088/1361-6420/aa635f. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse problem; Nonlocal diffusion; Nonlinear reaction; Ill-posed problem; Population density; Quasi-reversibility 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: | 06 Mar 2017 14:11 |
Last Modified: | 28 Feb 2018 01:38 |
Published Version: | https://doi.org/10.1088/1361-6420/aa635f |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1361-6420/aa635f |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:113192 |