Hussein, MS, Lesnic, D and Ivanchov, M (2013) Free boundary determination in nonlinear diffusion. East Asian journal on applied mathematics, 3 (4). 295 - 310. ISSN 2079-7362
Abstract
Free boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear leastsquares minimisation problem, which is solved numerically using the lsqnonl in routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, instability is manifest in the derivative of the moving free surface, but not in the free surface itself nor in the concentration or temperature.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | (c) 2013, Global Science Publications. First published in East Asian Journal on Applied Mathematics in volume 3, 2013 published by Global Science Press. This is an author produced version of a paper published in East Asian Journal on Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy |
Keywords: | Finite difference method; Free boundary problem; Nonlinear diffusion |
Dates: |
|
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: | 05 Nov 2014 14:40 |
Last Modified: | 15 Jan 2018 18:39 |
Published Version: | http://dx.doi.org/10.4208/eajam.100913.061113a |
Status: | Published |
Publisher: | Global Science Press |
Identification Number: | 10.4208/eajam.100913.061113a |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:81065 |