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A tractable mathematical model for tissue growth
journal contribution
posted on 2023-06-09, 19:37 authored by Joe Eyles, John R King, Vanessa StylesVanessa StylesUsing formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed interface evolving via forced mean curvature flow (together with a ‘kinetic under–cooling’ regularisation) where the forcing depends on the solution of a PDE that holds in the domain enclosed by the interface. We perform linear stability analysis and derive a diffuse–interface approximation of the model. Finite–element discretisations of two closely related models are presented, together with computational results comparing the approximate solutions.
History
Publication status
- Published
File Version
- Accepted version
Journal
Interfaces and Free BoundariesISSN
1463-9963Publisher
European Mathematical SocietyExternal DOI
Issue
4Volume
21Page range
463-493Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-11-22First Open Access (FOA) Date
2020-08-12First Compliant Deposit (FCD) Date
2019-11-11Usage metrics
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