Work

Long-time asymptotics of nonlinear Fokker-Planck equations with inhomogeneous diffusion and natural boundary conditions

Year: 2026

Type: preprint

Abstract: In this paper, we study the long-time asymptotics for nonlinear Fokker-Planck equations with spatial inhomogeneous diffusion, based on the law of energy dissipation. First, we derive a priori positive lower and upper bounds for solutions of the equations. Next, we give a sufficient condition for deriving the exponential decay of the dissipation function. Finally, we investigate whether the given sufficient condition is essential or not by numerical computation.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.05873

Authors: Araki, Kouta, Mizuno, Masashi

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: Construction of a new mathematical model of grain boundary motion and development in the theory of differential equations, Canonical mean curvature flow and its application to evolution problems

OpenAlex ID: W7212017431

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