Continuous dependence for a nonstandard Cahn-Hilliard system with nonlinear atom mobility

This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice [22]; it consists of the balance equations of microforces and microenergy; the two unknowns are the order parameter p and the chemical potential /mu. Some recent results obtained for this class of problems are reviewed and, in the case of a nonconstant and nonlinear atom mobility, uniqueness and continuous dependence on the initial data are shown with the help of a new line of argumentation developed in [13].