PreprintarXiv licencearXiv
Long-time asymptotics of nonlinear Fokker-Planck equations with inhomogeneous diffusion and natural boundary conditions
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.
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BibTeX
@misc{araki2026longtime,
title = {{Long-time asymptotics of nonlinear Fokker-Planck equations with inhomogeneous diffusion and natural boundary conditions}},
author = {Kouta Araki and Masashi Mizuno},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05873},
eprint = {2609.05873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05873},
}
RIS
TY - UNPB
TI - Long-time asymptotics of nonlinear Fokker-Planck equations with inhomogeneous diffusion and natural boundary conditions
AU - Kouta Araki
AU - Masashi Mizuno
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05873
UR - https://arxiv.org/abs/2609.05873
AB - 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.
ER -