Study of a system for the isothermal separation of components in a binary alloy with change of phase

An isothermal model describing the separation of the components of a binary metallic alloy is considered. A process of phase transition is also assumed to occur in the solder; hence, the state of the material is described by two order parameters, i.e. the concentration c of the first component and the phase field p. A physical derivation is provided starting from energy balance considerations. The resulting system of PDEs consists of a rather regular second-order parabolic equation for p coupled with a fourth-order relation of Cahn Hilliard type for c with constraint and solution-dependent mobility. Global existence of solutions is proved and several regularity properties are discussed under more restrictive assumptions on the physical parameters. Continuous dependence on data is shown in a special case. An asymptotic analysis of the model is also performed, yielding at the limit step a coupling of the original phase field equation with a Stefan-like system for c