We consider nonlinear stability for planar transition front solutions \(\bar{u} (x_1)\) arising in multidimensional (i.e., \(x\in {\mathbb {R}}^n\)) Cahn–Hilliard systems. In previous work, the author has established conditions under which such waves are spectrally and linearly stable, and in this analysis, it is shown that spectral stability implies nonlinear stability for such systems.
['Peter Howard']
Stability of Transition Front Solutions in Multidimensional Cahn–Hilliard Systems