  We propose and analyze a one-dimensional multi-species cross-diffusion system
with non-zero-flux boundary conditions on a moving domain, motivated by the
mod- eling of a Physical Vapor Deposition process. Using the boundedness by
entropy method, we prove the existence of a global weak solution to the
obtained system. In addition, existence of a solution to an optimal control
problem defined on the fluxes is established under the assumption that the
solution to the considered cross-diffusion system is unique. Lastly, we prove
that in the case when the imposed external fluxes are constant and positive and
the entropy density is defined as a classical logarithmic entropy, the
concentrations of the dif- ferent species converge in the long-time limit to
constant profiles at a rate inversely proportional to time. These theoretical
results are illustrated by numerical tests.
