Periodic solutions to Kobayashi--Warren--Carter systems

TL;DR

This paper proves the existence of time-periodic solutions to the Kobayashi--Warren--Carter system, a PDE model for grain boundary motion, avoiding previous restrictive assumptions.

Contribution

It provides a new proof of periodic solutions for the system without relying on compromised assumptions used in earlier research.

Findings

Existence of time-periodic solutions established

Proof avoids previous restrictive assumptions

Contributes to phase-field modeling of grain boundaries

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.