Global existence and uniqueness for a singular/degenerate Cahn-Hilliard system with viscosity
Abstract
Existence and uniqueness are investigated for 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. This system aims to model two-species phase segregation on an atomic lattice; in the balance equations of microforces and microenergy, the two unknowns are the order parameter and the chemical potential. A simpler version of the same system has recently been discussed in arXiv:1103.4585v1. In this paper, a fairly more general phase-field equation is coupled with a genuinely nonlinear diffusion equation. The existence of a global-in-time solution is proved with the help of suitable a priori estimates. In the case of a constant atom mobility, a new and rather unusual uniqueness proof is given, based on a suitable combination of variables.
Keywords
Cite
@article{arxiv.1205.4979,
title = {Global existence and uniqueness for a singular/degenerate Cahn-Hilliard system with viscosity},
author = {Pierluigi Colli and Gianni Gilardi and Paolo Podio-Guidugli and Jürgen Sprekels},
journal= {arXiv preprint arXiv:1205.4979},
year = {2012}
}
Comments
Key words: phase-field model, nonlinear laws, existence of solutions, new uniqueness proof