On nonlocal phase-field models

Abstract: We study nonlocal phase-field models for
temperature-dependent phase transitions with a
nonconserved order parameter. A typical example is
a solid-liquid transition. The model follows ideas
of Giacomin-Lebowitz and of Gajewski-Zacharias.
The basic assumption is that the free energy of the
system incorporates a nonlocal term modelling
long-distance interactions of the particles.

A derivation of the resulting coupled system of
integrodifferential equations is presented, and
the wellposedness of the system is proved. Also
the asymptotic behaviour of the solution will
be discussed.