Global Well-Posedness of a Nonlinear Fokker-Planck Type Model of Grain Growth

TL;DR

This paper proves the global well-posedness of a nonlinear Fokker-Planck system modeling grain boundary dynamics in polycrystalline materials, crucial for understanding microstructure evolution.

Contribution

It establishes the first rigorous mathematical proof of global existence and uniqueness for this nonlinear Fokker-Planck model related to grain growth.

Findings

Proved global well-posedness of the model

Linked the system to energy laws in grain boundary dynamics

Provided mathematical foundation for microstructure evolution modeling

Abstract

Most technologically useful materials spanning multiple length scales are polycrystalline. Polycrystalline microstructures are composed of a myriad of small crystals or grains with different lattice orientations which are separated by interfaces or grain boundaries. The changes in the grain and grain boundary structure of polycrystals highly influence the materials properties including, but not limited to, electrical, mechanical, and thermal. Thus, an understanding of how microstructures evolve is essential for the engineering of new materials. In this paper, we consider a recently introduced nonlinear Fokker-Planck-type system and establish a global well-posedness result for it. Such systems under specific energy laws emerge in the modeling of the grain boundary dynamics in polycrystals.