Periodic solutions to Kobayashi--Warren--Carter systems

Abstract: 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.