  Models of diffusive processes that occur on evolving domains are frequently
employed to describe biological and physical phenomena, such as diffusion
within expanding tissues or substrates. Previous investigations into these
models either report numerical solutions or require an assumption of linear
diffusion to determine exact solutions. Unfortunately, numerical solutions do
not reveal the relationship between the model parameters and the solution
features. Additionally, experimental observations typically report the presence
of sharp fronts, which are not captured by linear diffusion. Here we address
both limitations by presenting exact sharp-fronted solutions to a model of
degenerate nonlinear diffusion on a growing domain. We obtain the solution by
identifying a series of transformations that converts the model of a nonlinear
diffusive process on an evolving domain to a nonlinear diffusion equation on a
fixed domain, which admits known exact solutions for certain choices of
diffusivity functions. We determine expressions for critical time scales and
domain growth rates such that the diffusive population never reaches the domain
boundaries and hence the solution remains valid.
