Exponential convergence for ultrafast diffusion equations with log-concave weights
Analysis of PDEs
2025-07-18 v1
Abstract
We study the asymptotic behavior of a weighted ultrafast diffusion PDE on the real line, with a log-concave and log-lipschitz weight, and prove exponential convergence to equilibrium. This result goes beyond the compact setting studied in [22]. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in [11].
Cite
@article{arxiv.2507.13060,
title = {Exponential convergence for ultrafast diffusion equations with log-concave weights},
author = {Max Fathi and Mikaela Iacobelli},
journal= {arXiv preprint arXiv:2507.13060},
year = {2025}
}
Comments
12 pages