Singularity Time Scale of the Kardar–Parisi–Zhang Equation in 2+1 Dimensions

摘要

A master equation for the Kardar–Parisi–Zhang (KPZ) equation in 2+1 dimensions is developed. In the fully nonlinear regime we determine the finite time scale of the singularity formation in terms of the characteristics of forcing. The exact probability density function of the one point height field is obtained correspondingly.