Density  of Stochastic Cahn–Hilliard Equation and Its Approximation

The stochastic Cahn–Hilliard equation serves as an important phase-field model in materials science that describes phase separation processes in binary mixtures. In this chapter, we study the stochastic Cahn–Hilliard equation with polynomial nonlinearity and bounded noise diffusion, and approximate the density of its solution using a fully discrete finite difference method. The existence and convergence of the density of the numerical solution are established through a localization argument.