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The Cahn-Hilliard Model for the Kinetics of Phase Separation

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Mathematical Models for Phase Change Problems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 88))

Abstract

In this paper we consider the Cahn-Hilliard mathematical continuum model of spinodal decomposition (or phase separation) of a binary alloy. The phenomenological model is derived in section one. The existence theory for the Cahn-Hilliard equation is reviewed in section two. Various aspects and generalizations are surveyed in section three. A finite element approximation is studied in section four and, in particular, two fully discrete schemes are shown to possess Lyapunov functionals. Finally in section five some numerical simulations are described.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Sussex, BN1 9QH, Brighton, England

    C. M. Elliott

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  1. C. M. Elliott
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  1. Centro de Matemática e Aplicaçōes Fundamentais/INIC, Av. Prof. Gama Pinto, 2, 1699, Lisboa Codex, Portugal

    José Francisco Rodrigues

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© 1989 Birkhäuser Verlags Basel

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Elliott, C.M. (1989). The Cahn-Hilliard Model for the Kinetics of Phase Separation. In: Rodrigues, J.F. (eds) Mathematical Models for Phase Change Problems. International Series of Numerical Mathematics, vol 88. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9148-6_3

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  • DOI: https://doi.org/10.1007/978-3-0348-9148-6_3

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9926-0

  • Online ISBN: 978-3-0348-9148-6

  • eBook Packages: Springer Book Archive

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