arXiv subjects

Kouta Araki

Publications and source records attributed to Kouta Araki.

2 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2025

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

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.

math.AP↗