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. 
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     title = {Global {Existence} for a {Strongly} {Coupled} {Cahn-Hilliard} {System} with {Viscosity}},
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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/

[1] V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976. | MR | Zbl

[2] H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Math. Stud. 5, North-Holland, Amsterdam, 1973. | MR | Zbl

[3] P. Colli - G. Gilardi - P. Podio-Guidugli - J. Sprekels, Well-posedness and long-time behaviour for a nonstandard viscous Cahn-Hilliard system, SIAM J. Appl. Math., 71 (2011), 1849-1870. | DOI | MR | Zbl

[4] P. Colli - G. Gilardi - P. Podio-Guidugli - J. Sprekels, Global existence and uniqueness for a singular/degenerate Cahn-Hilliard system with viscosity, preprint WIAS-Berlin n. 1713 (2012), 1-28. | DOI | MR

[5] P. Podio-Guidugli, Models of phase segregation and diffusion of atomic species on a lattice, Ric. Mat., 55 (2006), 105-118. | DOI | MR | Zbl

[6] J. Simon, Compact sets in the space $L^p(0; T; B)$, Ann. Mat. Pura Appl. (4), 146 (1987), 65-96. | DOI | MR | Zbl