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Title: Global existence for a strongly coupled Cahn-Hilliard system with viscosity : in memory of Enrico Magenes
Authors: Colli, PierluigiGilardi, GianniPodio-Guidugli, PaoloSprekels, JürgenMagenes, Enrico
Issue Date: 2012
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1691, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: 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 [CGPS11]. Both systems conform to the general theory developed in [Pod06]: 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 [CGPS11] is coupled with a highly nonlinear diffusion equation for $mu$, in which the conductivity coefficient is allowed to depend nonlinearly on both variables.
Keywords: Viscous Cahn–Hilliard system; phase field model; nonlinear conductivity; existence of solutions
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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