On the exponential convergence to equilibrium for ultrafast diffusion equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912580376723456 |
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| author | Huang, Yi C. Tong, Xinhang |
| author_facet | Huang, Yi C. Tong, Xinhang |
| contents | We propose a simple proof of the exponential convergence to equilibrium for ultrafast diffusion equations in $\mathbb{R}^n$. Our approach, based on the direct use of Poincaré inequality, gets rid of the optimal transport arguments used in \cite{fathi2025} which are valid for Gaussian-excluded one-dimensional weights. This simplification allows us to extend their results to Gaussian measures in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the exponential convergence to equilibrium for ultrafast diffusion equations Huang, Yi C. Tong, Xinhang Analysis of PDEs Classical Analysis and ODEs We propose a simple proof of the exponential convergence to equilibrium for ultrafast diffusion equations in $\mathbb{R}^n$. Our approach, based on the direct use of Poincaré inequality, gets rid of the optimal transport arguments used in \cite{fathi2025} which are valid for Gaussian-excluded one-dimensional weights. This simplification allows us to extend their results to Gaussian measures in higher dimensions. |
| title | On the exponential convergence to equilibrium for ultrafast diffusion equations |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.07382 |