Long-time asymptotic behavior of nonlinear Fokker-Planck type equations with periodic boundary conditions

2024/04/08 by Yekaterina Epshteyn, Chun Liu, Epshteyn, Yekaterina +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2404.05157

openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the asymptotic behavior of a class of nonlinear Fokker-Planck type equations in a bounded domain with periodic boundary conditions. The system is motivated by our study of grain boundary dynamics, especially under the non-isothermal environments. To obtain the long time behavior of the solutions, in particular, the exponential decay, the kinematic structures of the systems are investigated using novel reinterpretation of the classical entropy method.

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