An analytic solution for a Gompertz-like reaction-diffusion model for tumour growth

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.