Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory

John E. Hutchinson*, Yoshihiro Tonegawa

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    123 Citations (Scopus)

    Abstract

    We study the general asymptotic behavior of critical points, including those of non-minimal energy type, of the functional for the van der Waals-Cahn-Hilliard theory of phase transitions. We prove that the interface is close to a hypersurface with mean curvature zero when no Lagrange multiplier is present, and with locally constant mean curvature in general. The energy density of the limiting measure has integer multiplicity almost everywhere modulo division by a surface energy constant.

    Original languageEnglish
    Pages (from-to)49-84
    Number of pages36
    JournalCalculus of Variations and Partial Differential Equations
    Volume10
    Issue number1
    DOIs
    Publication statusPublished - Jan 2000

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