Colli, Pierluigi and Gilardi, Gianni and Podio-Guidugli, Paolo and Sprekels, Jürgen:
Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.3, p. 495-513, (English)
pdf (328 Kb), djvu (171 Kb). | MR 3051734 | Zbl 1285.35080
Sunto
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 [3]. Both systems conform to the general theory developed in [5]: 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 [3] is coupled with a highly nonlinear diffusion equation for $\mu$, in which the diffusivity coefficient is allowed to depend nonlinearly on both variables.
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