Instability in a continuum kinetic-growth model with surface relaxation

We study the recently proposed nonlinear kinetic-growth model with surface relaxation for molecular-beam epitaxy in both two (2D) and three (3D) dimensions. We find that the dynamics of the equation without noise is nonlinearly unstable, in contrast to the dynamics of the Kardar-Parisi-Zhang equation. Because of the large fluctuation exponent in 2D, one important consequence is that there exists a strong-coupling regime where the interface develops a local divergence in finite time. For 3D or higher dimensions, the fluctuation is not strong enough to drive the system towards divergence, and the scaling is correctly given by renormalization-group calculations.