Author:
DANILOV V. G.,OMEL'YANOV G. A.,RADKEVICH E. V.
Abstract
We consider a new concept of weak solutions to the phase-field
equations with a small
parameter ε characterizing the length of interaction. For the standard
situation of a single
free interface, this concept (in contrast with the common one) leads to
the well-known
Stefan–Gibbs–Thomson problem as ε→0. For the case
of a large number M(ε) (M(ε)→∞ as
ε→0)
of free interfaces, which corresponds to the ‘wave-train’
interpretation of a ‘mushy
region’, this concept allows us to obtain the limit problem as ε→0.
Publisher
Cambridge University Press (CUP)
Cited by
33 articles.
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