Convergence of phase interfaces in the Van der Waals-Cahn-Hilliard theory
John E. Hutchinson and Yoshihiro Tonegawa
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.
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