  We investigate the time evolution of an initial step profile separating a
bare substrate region from the rest of the compressively strained adsorbate
layer near a commensurate to incommensurate transition. The rate of profile
evolution as a function of the mismatch, coverage and the strength of the
substrate potential are determined by Brownian molecular dynamics simulations.
We find that the results are qualitatively similar to those observed for the
Pb/Si(111) system. The anomalously fast time evolution and sharpness of the
non-equilibrium profile can be understood through the domain wall creation at
the boundary and its subsequent diffusion into the interior of the adsorbate
layer.
