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Title: Global existence and uniqueness for a singular/degenerate Cahn-Hilliard system with viscosity
Authors: Colli, PierluigiGilardi, GianniPodio-Guidugli, PaoloSprekels, Jürgen
Issue Date: 2012
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1713, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: 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 [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 costant atom mobility, a new and rather unusual uniqueness proof is given, based on a suitable combination of variables.
Keywords: Phase-field model; nonlinear laws; existence of solutions; new uniqueness proof
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
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Appears in Collections:Mathematik



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