Work

Existence and Ergodicity for Nonlinear Fokker-Planck Equations for Probability Density Functions

Year: 2026

Type: preprint

Abstract: For a class of nonlinear Fokker-Planck equations for probability densities, we construct distributional solutions by using an approximation scheme with nonlinear Neumann problems in balls. Moreover, we introduce nonlinear functional inequalities to estimate the convergence rates of the distributional solutions to the stationary solution, with respect to the $p$-variance for $p\in [1,2]$ including the relative entropy $(p=1)$ and the variance $(p=2)$. These nonlinear functional inequalities are then established in both non-degenerate and degenerate settings, so that the main results are applied to a number of typical models with various convergence rates.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.01245

Authors: Huang, Xing, Röckner, Michael, Wang, Feng-Yu

Institution: Tianjin University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China

Awards: G1288578048, G2553373668, G6405730534, SFB 1283: Unsicherheit beherrschen und Zufall sowie Unordnung nutzen in Analysis, Stochastik und deren Anwendungen

OpenAlex ID: W7215700622

Cites: 1

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Related to: 10