The morphology of crystalline thin films evolving on flat rigid substrates by
condensation of extra film atoms or by evaporation of their own atoms in the
surrounding vapor is studied in the framework of the theory of stress driven
rearrangement instabilities (SDRI). By following the literature both the elastic
contributions due to the mismatch between the film and the substrate lattices at
their theoretical (free-standing) elastic equilibrium, and a curvature perturbative
regularization preventing the problem to be ill-posed due to the otherwise exhibited
backward parabolicity, are added in the evolution equation. The resulting Cauchy
problem under investigation consists of an anisotropic mean-curvature type flow of
the fourth-order on the film profiles, which are assumed to be parametrizable as
graphs of functions measuring the film thicknesses, coupled with a quasistatic elastic
problem in the film bulks. The existence of a regular solution for a finite period of
time is established under periodic boundary conditions by means of employing
minimizing movements to exploit the gradient-flow structure of the evolution
equation.
