We examine the passage from Burton-Cabrera-Frank (BCF) type models in epitaxial growth to continuum equations describing the evolution of the film height profiles as well as the adatom densities. The equations we obtain are in the form of a coupled system of diffusion equations for the adatom density and a Hamilton-Jacobi equation for the film height. This is supplemented with appropriate boundary conditions to describe the dynamics of the peaks and valleys on the surface of the
film. Some numerical simulations will be shown to describe the surface profile near the nucleation sites. In particular, they show the persistence of some traveling wave patterns.
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