Long-time behavior of free energy in the nonlinear Fokker-Planck equation

Kouta Araki; Masashi Mizuno

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arXiv · 2512.11455

Long-time behavior of free energy in the nonlinear Fokker-Planck equation

Kouta Araki·Masashi Mizuno

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Abstract

We study the asymptotic behavior of Fokker-Planck equations with spatially inhomogeneous nonlinear diffusion, based on the energy dissipation law. First, we consider the Fokker-Planck equation with porous-medium-type nonlinear diffusion that satisfies the energy dissipation law by introducing spatial inhomogeneity into the free energy. We obtain a result on the long-time behavior of the dissipation function for sufficiently large diffusion coefficients by extending the entropy dissipation method to the case of inhomogeneous diffusion.

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Kouta Araki, Masashi Mizuno. 2025-12-12. Long-time behavior of free energy in the nonlinear Fokker-Planck equation. https://arxiv.org/abs/2512.11455

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