WIAS Preprint No. 1691, (2012)

Global existence for a strongly coupled Cahn--Hilliard system with viscosity

Authors

• Colli, Pierluigi
• Gilardi, Gianni
• Podio-Guidugli, Paolo
• Sprekels, Jürgen

2010 Mathematics Subject Classification

• 74A15 35K61 35A05 35B40

Keywords

• viscous Cahn-Hilliard system, phase field model, nonlinear conductivity, existence of solution

DOI

10.20347/WIAS.PREPRINT.1691

Abstract

An existence result is proved 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 is meant to model two-species phase segregation on an atomic lattice under the presence of diffusion. A similar system has been recently introduced and analyzed in [CGPS11]. Both systems conform to the general theory developed in [Pod06]: two parabolic PDEs, interpreted as balances of microforces and microenergy, are to be solved for the order parameter $rho$ and the chemical potential $mu$. In the system studied in this note, a phase-field equation in $rho$ fairly more general than in [CGPS11] is coupled with a highly nonlinear diffusion equation for $mu$, in which the conductivity coefficient is allowed to depend nonlinearly on both variables.

Appeared in

• Boll. Unione Mat. Ital. (9), 5 (2012) pp. 495--513.