Global existence for a strongly coupled Cahn-Hilliard system with viscosity : in memory of Enrico Magenes

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.