A tractable mathematical model for tissue growth

Eyles, Joe, King, John R and Styles, Vanessa (2019) A tractable mathematical model for tissue growth. Interfaces and Free Boundaries, 21 (4). pp. 463-493. ISSN 1463-9963 (Accepted)

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Abstract

Using 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Amelia Redman
Date Deposited: 22 Nov 2019 11:25
Last Modified: 09 Jan 2020 14:45
URI: http://sro.sussex.ac.uk/id/eprint/87986

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