Geodesic
Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 495-513

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
@article{BUMI_2012_9_5_3_a2,
     author = {Colli, Pierluigi and Gilardi, Gianni and Podio-Guidugli, Paolo and Sprekels, J\"urgen},
     title = {Global {Existence} for a {Strongly} {Coupled} {Cahn-Hilliard} {System} with {Viscosity}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {495--513},
     publisher = {mathdoc},
     volume = {Ser. 9, 5},
     number = {3},
     year = {2012},
     zbl = {1285.35080},
     mrnumber = {3051734},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a2/}
}
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Colli, Pierluigi; Gilardi, Gianni; Podio-Guidugli, Paolo; Sprekels, Jürgen. Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 495-513. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a2/