PDE 12: Cahn–Hilliard equation

This equation is a dissipative PDE

\[\frac{\partial u}{\partial t}=\frac{\partial^2 }{\partial_x^2}(p u+r u^3+qu_{xx}), \] where \( u=u(x,t)\) You could consider periodic boundary conditions.

Google: Cahn-Hilliard equation (!)

Challenges: non-linearity, high order derivatives.