Spinodal Decomposition for Multi-component Cahn-hilliard Systems

We consider the initial stage phase separation process in multi-component CahnHilliard systems through spinodal decomposition. Relying on recent work of MaierPaape and Wanner we establish the existence of certain dominating subspaces determining the behavior of most solutions originating near a spatially homogeneous state. It turns out that depending on the initial concentrations of the alloy components, several distinct phenomena can be observed. For ternary alloys we observe the following two phenomena: If the initial concentrations of the three components are almost equal, the dominating subspace consists of two copies of the nite-dimensional dominating subspace from the binary alloy case. For all other initial concentrations, only one copy of the binary dominating subspace determines the behavior. Thus, in the latter case we observe a strong mutual coupling of the concentrations in the alloy during the initial separation process. AMS subject classi cations: 35K50, 35B05, 35P10, 35Q72, 73B30, 82B26.