  In this paper, a system of parabolic PDEs, called the
Kobayashi--Warren--Carter system, is considered as a possible phase-field model
of planar grain boundary motion. The Main Theorem is concerned with the
existence of a time-periodic solution to the Kobayashi--Warren--Carter system,
and the principal objective is to provide a proof without the use of a
compromised assumption, which researchers have been forced to adopt in recent
studies.

Analysis of PDEs