Spectral analysis of planar transition fronts for the Cahn–Hilliard equation

We consider the spectrum of the linear operator that arises upon linearization of the Cahn–Hilliard equation in dimensions d⩾2 about a planar transition front (a solution that depends on only one distinguished space variable and that has different values at ±∞). In previous work the author has established conditions on this spectrum under which such planar transition fronts are asymptotically stable, and we verify here that those conditions hold for all such waves arising in a general form of the Cahn–Hilliard equation.