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; it consists of the balance equations of microforces and microenergy; the two unknowns are the order parameter and the chemical potential . Some recent results obtained for this class of problems is 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.