抄録
The Edwards-Wilkinson (EW) equation is a stochastic partial differential equation which mathematically models the growing rough surfaces. It has been pointed out that the variance of the solution of the EW equation diverges in spatial dimensions equal to or larger than 2. Based on mathematical and numerical analyses for the EW equation, we give two means to avoid the divergence. The first one is the smoothing of the EW equation by introducing a fourth order derivative. The second is to replace the Gaussian white noise with a less singularly correlated noise. These are confirmed by numerical calculations, and suggest a more reasonable modelling for the growing rough surface phenomenon.
