Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model
A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady but the other is not. A complete Lie symmetry classification,...
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| Format: | Article |
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MDPI
2018
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| Online Access: | https://eprints.nottingham.ac.uk/52221/ |
| _version_ | 1848798676402569216 |
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| author | Cherniha, Roman Davydovych, Vasyl King, John R. |
| author_facet | Cherniha, Roman Davydovych, Vasyl King, John R. |
| author_sort | Cherniha, Roman |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady but the other is not. A complete Lie symmetry classification, including a number of the cases characterised as being unlikely to be identified purely by intuition, is obtained. Notably, in addition to the symmetry analysis of the PDEs themselves, the approach is extended to allow the derivation of exact solutions to specific moving-boundary problems motivated by biological applications (tumour growth). Graphical representations of the solutions are provided and a biological interpretation is briefly addressed. The results are generalised on multi-dimensional case under the assumption of the radially symmetrical shape of the tumour. |
| first_indexed | 2025-11-14T20:23:33Z |
| format | Article |
| id | nottingham-52221 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:23:33Z |
| publishDate | 2018 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-522212020-05-04T19:36:53Z https://eprints.nottingham.ac.uk/52221/ Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model Cherniha, Roman Davydovych, Vasyl King, John R. A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady but the other is not. A complete Lie symmetry classification, including a number of the cases characterised as being unlikely to be identified purely by intuition, is obtained. Notably, in addition to the symmetry analysis of the PDEs themselves, the approach is extended to allow the derivation of exact solutions to specific moving-boundary problems motivated by biological applications (tumour growth). Graphical representations of the solutions are provided and a biological interpretation is briefly addressed. The results are generalised on multi-dimensional case under the assumption of the radially symmetrical shape of the tumour. MDPI 2018-05-17 Article PeerReviewed Cherniha, Roman, Davydovych, Vasyl and King, John R. (2018) Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model. Symmetry, 10 (5). 171/1-171/21. ISSN 2073-8994 Lie symmetry classification; Exact solution; Nonlinear reaction-diffusion system; Tumour growth model; Moving-boundary problem https://doi.org/10.3390/sym10050171 doi:10.3390/sym10050171 doi:10.3390/sym10050171 |
| spellingShingle | Lie symmetry classification; Exact solution; Nonlinear reaction-diffusion system; Tumour growth model; Moving-boundary problem Cherniha, Roman Davydovych, Vasyl King, John R. Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model |
| title | Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model |
| title_full | Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model |
| title_fullStr | Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model |
| title_full_unstemmed | Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model |
| title_short | Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model |
| title_sort | lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model |
| topic | Lie symmetry classification; Exact solution; Nonlinear reaction-diffusion system; Tumour growth model; Moving-boundary problem |
| url | https://eprints.nottingham.ac.uk/52221/ https://eprints.nottingham.ac.uk/52221/ https://eprints.nottingham.ac.uk/52221/ |