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arXiv · 2407.06757

Extinction profiles for the Sobolev critical fast diffusion equation in bounded domains. I. One bubble dynamics

Tianling Jin·Jingang Xiong
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Abstract

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.

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Tianling Jin, Jingang Xiong. 2024-07-09. Extinction profiles for the Sobolev critical fast diffusion equation in bounded domains. I. One bubble dynamics. https://arxiv.org/abs/2407.06757

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