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
2026-04-01 08:26:09.1775031969
The PDE $u_t = -\Delta^2 u -\Delta u + f$
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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.