Cahn–Hilliard equation

We now study the Cahn–Hilliard equation with an extra reaction term,

\[\pd{u}{t} = r\nabla^2 (u^3-u-g\nabla^2u)+u-u^3,\]

with periodic boundary conditions.

There are lots of things that you can do with this equation (with or without the reaction term). For instance, you can extend it to a ‘non-reciprocal’ Cahn–Hilliard system as in Brauns and Marchetti, which exhibits pretty patterns that you can play with in this interactive simulation. Thanks to Lloyd Fung for pointing out this example!