Local well-posedness of a nonlinear Fokker-Planck model
Yekaterina Epshteyn, Chang Liu, Chun Liu, and Masashi Mizuno
TL;DR
This paper proves local well-posedness for a new nonlinear Fokker-Planck equation, which models grain boundary dynamics in microstructure evolution of polycrystalline materials, highlighting its mathematical and physical significance.
Contribution
It establishes the local well-posedness of a novel nonlinear Fokker-Planck equation relevant to material science applications.
Findings
Proved local existence and uniqueness of solutions.
Connected the equation to physical models of microstructure evolution.
Highlighted energy law properties of the equation.
Abstract
Noise or fluctuations play an important role in the modeling and understanding of the behavior of various complex systems in nature. Fokker-Planck equations are powerful mathematical tool to study behavior of such systems subjected to fluctuations. In this paper we establish local well-posedness result of a new nonlinear Fokker-Planck equation. Such equations appear in the modeling of the grain boundary dynamics during microstructure evolution in the polycrystalline materials and obey special energy laws.
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Taxonomy
TopicsProbabilistic and Robust Engineering Design · Theoretical and Computational Physics · Material Dynamics and Properties