Figure 1

Schematic wavelength-amplitude diagrams for the stationary solutions of period $\lambda$ and amplitude $A$. The four scenarios refer to different behaviors for ${\lambda }^{\prime }(A)$, as explained in the main text. The linear stability analysis of the trivial solution $u=0$ is represented by the line $A=0$: stability (full line) for $\lambda <{\lambda }_0=2\pi$ and instability (dashed line) for $\lambda >{\lambda }_0$. For the conserved models the flat interface starts to develop a profile of period ${\lambda }_c=\sqrt{2}{\lambda }_0$ (see the big dotted arrows close to the $\lambda$ axis). In cases (ii)–(iv) a coarsening process takes place, but in case (iii) it stops when $\lambda (A)$ attains the maximum (interrupted coarsening) and the amplitude starts growing (see the big dotted arrow close to the maximum).Reuse & Permissions