Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity
Colli, Pierluigi ; Gilardi, Gianni ; Podio-Guidugli, Paolo ; Sprekels, Jürgen
Bollettino dell'Unione Matematica Italiana, Tome 5 (2012), p. 495-513 / Harvested from Biblioteca Digitale Italiana di Matematica
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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 ρ and the chemical potential μ. In the system studied in this note, a phase-field equation in ρ fairly more general than in [3] is coupled with a highly nonlinear diffusion equation for μ, in which the diffusivity coefficient is allowed to depend nonlinearly on both variables.

Publié le : 2012-10-01
@article{BUMI_2012_9_5_3_495_0,
     author = {Pierluigi Colli and Gianni Gilardi and Paolo Podio-Guidugli and J\"urgen Sprekels},
     title = {Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5},
     year = {2012},
     pages = {495-513},
     zbl = {1285.35080},
     mrnumber = {3051734},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_3_495_0}
}

Colli, Pierluigi; Gilardi, Gianni; Podio-Guidugli, Paolo; Sprekels, Jürgen. Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 495-513. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_3_495_0/

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