Long-time behavior of free energy in the nonlinear Fokker-Planck equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917146447052800 |
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| author | Araki, Kouta Mizuno, Masashi |
| author_facet | Araki, Kouta Mizuno, Masashi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_11455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-time behavior of free energy in the nonlinear Fokker-Planck equation Araki, Kouta Mizuno, Masashi Analysis of PDEs Primary 35B40, Secondary 35A15, 35A09, 35B09, 35K20, 35K55, 35K65, 35Q84 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. |
| title | Long-time behavior of free energy in the nonlinear Fokker-Planck equation |
| topic | Analysis of PDEs Primary 35B40, Secondary 35A15, 35A09, 35B09, 35K20, 35K55, 35K65, 35Q84 |
| url | https://arxiv.org/abs/2512.11455 |