(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Colli, Pierluigi; Gilardi, Gianni; Podio-Guidugli, Paolo; Sprekels, Jürgen
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 [Podio-Guidugli 2006]; it
consists of the balance equations of microforces and microenergy; the two
unknowns are the order parameter $rho$ and the chemical potential $mu$. 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 developed in Colli/Gilardi/Podio-Guidugli/Sprekels 2012.
