Cahn–Hilliard equation

Summary

The Cahn–Hilliard equation is the fourth-order parabolic equation $c_t = \Delta(c^3 - c - \gamma \Delta c)$. It describes how a mixture of two substances separates into regions rich in one or the other. Unlike the Allen–Cahn equation, it conserves the total amount $\int c\,dx$. It is the gradient flow of the Ginzburg–Landau energy in the $H^{-1}$ metric.