Exponential convergence for ultrafast diffusion equations with log-concave weights

Q: What type of study is this?

This is a Quantitative Study study.

Max Fathi; Mikaela Iacobelli

doi:10.48550/arxiv.2507.13060

July 17, 2025Open Access

Exponential convergence for ultrafast diffusion equations with log-concave weights

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Key Points

Exponential convergence to equilibrium is established, indicating stability in ultrafast diffusion equations.
The analysis extends results from compact settings, addressing broader mathematical implications.
Focus is placed on log-concave and log-lipschitz weights, emphasizing their significance in the convergence behavior.
The gradient flow approach illuminates the connection to quantization of measures, offering deeper insights into the underlying mechanisms.

Implication

Analysis reveals exponential convergence to equilibrium in ultrafast diffusion PDEs, highlighting implications for quantization of measures.

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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Cite This Study

Fathi et al. (2025) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc69710d https://doi.org/10.48550/arxiv.2507.13060

View Full Paper

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Exponential convergence for ultrafast diffusion equations with log-concave weights

Key Points

Implication

Abstract

Discussion

Cite This Study

Exponential convergence for ultrafast diffusion equations with log-concave weights

Key Points

Implication

Abstract

Discussion

Cite This Study

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