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

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.

References in corpus (4)

• A new Fokker-Planck approach for relaxation-driven evolution of galactic nuclei
• Learning macroscopic internal variables and history dependence from microscopic models
• Relative Grain Boundary Energies from Triple Junction Geometry: Limitations to Assuming the Herring Condition in Nanocrystalline Thin Films
• Local well-posedness of a nonlinear Fokker-Planck model