An analytic solution for a Gompertz-like reaction-diffusion model for tumour growth
Date
2020
Authors
Bradshaw Hajek, B.H.
Broadbridge, P.
Editors
Giga, Y.
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Conference paper
Citation
The Role of Metrics in the Theory of Partial Differential Equations, 2020 / Giga, Y. (ed./s), vol.85, pp.127-136
Statement of Responsibility
Conference Name
11th Mathematical Society of Japan, Seasonal Institute, The role of metrics in the theory of partial differential equations (2 Jul 2018 - 13 Jul 2018 : Sapporo, Japan)
Abstract
Here, we construct spherically symmetric exact analytic solutions to a reaction-diffusion model for tumour growth with a Gompertz-like growth term. This is achieved by making use of a nonclassical symmetry that is valid whenever the nonlinear reaction term and the nonlinear diffusivity satisfy a particular relationship. Example solutions are given in two different cases. In the first, the tumour size and the cell density within the tumour change, while in the second, the cell density changes but the tumour size remains constant.