Local well-posedness of a nonlinear Fokker–Planck model. (1st March 2023)

• Record Type: Journal Article
• Authors: Epshteyn, Yekaterina; Liu, Chang; Liu, Chun; Mizuno, Masashi
• Is Part Of: Nonlinearity. Volume 36:Number 3(2023)
• Page Start: 1890
• Page End: 1917
• Publication Date: 2023-03-01
• Subjects: nonlinear Fokker–Planck equation -- energy law -- energetic-variational approach -- nonlinearity of the critical order -- local-wellposedness; 35A01 -- 35A02 -- 35K15 -- 35Q84 -- 60J60; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/acb7c2
• Languages: English
• ISSNs: 0951-7715

Abstract

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 tools 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.