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

Please always quote using this URN:urn:nbn:de:0296-matheon-12274
  • 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 conductivity coefficient is allowed to depend nonlinearly on both variables.

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Metadaten
Author:Pierluigi Colli, Gianni Gilardi, Paolo Podio-Guidugli, Jürgen Sprekelsp
URN:urn:nbn:de:0296-matheon-12274
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/05/29
Release Date:2013/05/29
Tag:existence of solutions; nonlinear conductivity; phase field model; viscous Cahn-Hilliard system
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B40 Asymptotic behavior of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equations
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids / 74A15 Thermodynamics
Preprint Number:1021
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