  The aim of this note is to present preliminary existence results for a system
of cross-diffusion equations defined on a domain with moving boundaries, which
model the evolution of the concentrations of different chemical species in a
solid during a Chemical Vapor Deposition process. The system of equations, when
the domain remains fixed over time, can be seen formally as a gradient flow
system which can be analyzed using the boundedness by entropy method introduced
by Burger and J\"ungel. Preliminary existence results are presented in the case
of a one-dimensional moving boundary domain.
