Brander, T, Lesnic, D orcid.org/0000-0003-3025-2770 and Cao, K (2023) Inverse problems for a model of biofilm growth. The IMA Journal of Applied Mathematics, 88 (2). pp. 258-281. ISSN 0272-4960
Abstract
A bacterial biofilm is an aggregate of micro-organisms growing fixed onto a solid surface, rather than floating freely in a liquid. Biofilms play a major role in various practical situations such as surgical infections and water treatment. We consider a non-linear partial differential equation (PDE) model of biofilm growth subject to initial and Dirichlet boundary conditions, and the inverse coefficient problem of recovering the unknown parameters in the model from extra measurements of quantities related to the biofilm and substrate. By addressing and analysing this inverse problem, we provide reliable and robust reconstructions of the primary physical quantities of interest represented by the diffusion coefficients of substrate and biofilm, the biomass spreading parameters, the maximum specific consumption and growth rates, the biofilm decay rate and the half saturation constant. We give particular attention to the constant coefficients involved in the leading-part non-linearity, and present a uniqueness proof and some numerical results. In the course of the numerical investigation, we have identified extra data information that enables improving the reconstruction of the eight-parameter set of physical quantities associated to the model of biofilm growth.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/ 4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | biofilm; inverse problem; uniqueness; parameter estimation; reaction–diffusion system; degenerate parabolic system |
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: | 24 Jan 2023 14:20 |
Last Modified: | 08 Feb 2024 03:23 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imamat/hxad008 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:195439 |