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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].

Keywords

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

R2 v1 2026-07-01T04:05:58.020Z