Shadowing instability in three dimensions

We study a nonequilibrium interface growth model that includes the nonlocal shadowing effect in three spatial dimensions. The model is represented by a stochastic partial differential equation for the local growth rate of an interface. The nonlocal effect is modeled by a term in the growth rate that is proportional to the local exposure angle. This leads to a shadowing instability, and the interface develops into a mountain landscape which coarsens in time. The structure factor of the interface shape shows a dynamic scaling form. The scaling exponents are computed.