Continuous dependence for a nonstandard Cahn--Hilliard system with nonlinear atom mobility
- Colli, Pierluigi
- Gilardi, Gianni
- Podio-Guidugli, Paolo
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35K61 35A05 74A15
- phase-field model, nonlinear system of partial differential equations, existence of solutions, new uniqueness proof
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.
- Rend. Semin. Mat. Univ. Politec. Torino, 70 (2012) pp. 27--52.