  Reaction-diffusion equations are widely used as the governing evolution
equations for modeling many physical, chemical, and biological processes. Here
we derive reaction-diffusion equations to model transport with reactions on a
one-dimensional domain that is evolving. The model equations, which have been
derived from generalized continuous time random walks, can incorporate
complexities such as subdiffusive transport and inhomogeneous domain stretching
and shrinking. A method for constructing analytic expressions for short time
moments of the position of the particles is developed and moments calculated
from this approach are shown to compare favourably with results from random
walk simulations and numerical integration of the reaction transport equation.
The results show the important role played by the initial condition. In
particular, it strongly affects the time dependence of the moments in the short
time regime by introducing additional drift and diffusion terms. We also
discuss how our reaction transport equation could be applied to study the
spreading of a population on an evolving interface.
