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<p>In this paper, we investigate the extinction behavior of nonnegative solutions to the Sobolev critical fast diffusion equation in bounded smooth domains with the Dirichlet zero boundary condition. Under the two-bubble energy threshold assumption on the initial data, we prove the dichotomy that every solution converges uniformly, in terms of relative error, to either a steady state or a blowing-up bubble.</p>

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Extinction Profiles for the Sobolev Critical Fast Diffusion Equation in Bounded Domains. I. One Bubble Dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月11日

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  • Tianling Jin,
  • Jingang Xiong

摘要

In this paper, we investigate the extinction behavior of nonnegative solutions to the Sobolev critical fast diffusion equation in bounded smooth domains with the Dirichlet zero boundary condition. Under the two-bubble energy threshold assumption on the initial data, we prove the dichotomy that every solution converges uniformly, in terms of relative error, to either a steady state or a blowing-up bubble.