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Existence and Ergodicity for Nonlinear Fokker-Planck Equations for Probability Density Functions
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∈ [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.
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BibTeX
@misc{huang2026existence,
title = {{Existence and Ergodicity for Nonlinear Fokker-Planck Equations for Probability Density Functions}},
author = {Xing Huang and Michael Röckner and Feng-Yu Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01245},
eprint = {2610.01245},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01245},
}
RIS
TY - UNPB
TI - Existence and Ergodicity for Nonlinear Fokker-Planck Equations for Probability Density Functions
AU - Xing Huang
AU - Michael Röckner
AU - Feng-Yu Wang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01245
UR - https://arxiv.org/abs/2610.01245
AB - 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∈ [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.
ER -