# The PDE $u_t = -\Delta^2 u -\Delta u + f$

Does the PDE $u_t = -\Delta^2 u -\Delta u + f$ have a physical use or meaning? I am asking specifically about the the Laplace term after the biLaplace term.. is it unusual or "unnecessary" in some way to have both terms at the same time?

Thank you

This is the linearization of th Cahn-Hilliard equation about a constant state. The equation is used to model phase separation in binary mixtures and alloys. The quantity $u$ then is a volume fraction.