On the exponential convergence to equilibrium for ultrafast diffusion equations

Yi C. Huang; Xinhang Tong

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arXiv · 2509.07382

On the exponential convergence to equilibrium for ultrafast diffusion equations

Yi C. Huang·Xinhang Tong

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Abstract

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 Poincar\'e 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.

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Yi C. Huang, Xinhang Tong. 2025-09-09. On the exponential convergence to equilibrium for ultrafast diffusion equations. https://arxiv.org/abs/2509.07382

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