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Global existence and uniqueness for a singular/degenerate Cahn-Hilliard system with viscosity

Please always quote using this URN:urn:nbn:de:0296-matheon-12261
  • Existence and uniqueness are investigated 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 aims to model two-species phase segregation on an atomic lattice [19]; in the balance equations of microforces and microenergy, the two unknowns are the order parameter rho and the chemical potential mu. A simpler version of the same system has recently been discussed in [8]. In this paper, a fairly more general phase-field equation for rho is coupled with a genuinely nonlinear diffusion equation for mu. The existence of a global-in-time solution is proved with the help of suitable a priori estimates. In the case of constant atom mobility, a new and rather unusual uniqueness proof is given, based on a suitable combination of variables.

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Metadaten
Author:Pierluigi Colli, Gianni Gilardi, Paolo Podio-Guidugli, Jürgen Sprekels
URN:urn:nbn:de:0296-matheon-12261
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; new uniqueness proof; nonlinear laws; phase-field model
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification: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:1020
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