Work

Global well-posedness of a nonlinear Fokker-Planck type model of grain growth

Year: 2025

Type: article

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 material's 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.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025146

Authors: Batuhan Bayir, Yekaterina Epshteyn, William M Feldman

Institution: University of Utah

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Science Foundation Ireland

Awards: Free Boundary Geometry in Heterogeneous Media, Collaborative Research: DMREF: Microstructure by Design: Integrating Grain Growth Experiments, Data Analytics, Simulation, and Theory