Exponential convergence for ultrafast diffusion equations with log-concave weights

Max Fathi; Mikaela Iacobelli

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arXiv · 2507.13060

Exponential convergence for ultrafast diffusion equations with log-concave weights

Max Fathi·Mikaela Iacobelli

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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].

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Max Fathi, Mikaela Iacobelli. 2025-07-17. Exponential convergence for ultrafast diffusion equations with log-concave weights. https://arxiv.org/abs/2507.13060

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