Surface Roughness in Molecular Beam Epitaxy.

This paper discusses the roughness of surfaces described by nonlinear stochastic partial differential equations on bounded domains. Roughness is an important characteristic for processes arising in molecular beam epitaxy, and is usually described by the mean interface width of the surface, i.e. the expected value of the squared Lebesgue norm. By employing results on the mean interface width for linear stochastic partial differential equations perturbed by colored noise, which have been previously obtained, we describe the evolution of the surface roughness for two classes of nonlinear equations, asymptotically both for small and large times. [ABSTRACT FROM AUTHOR]