Extinction profiles for the Sobolev critical fast diffusion equation in bounded domains. I. One bubble dynamics
Analysis of PDEs
2024-07-10 v1
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.
Cite
@article{arxiv.2407.06757,
title = {Extinction profiles for the Sobolev critical fast diffusion equation in bounded domains. I. One bubble dynamics},
author = {Tianling Jin and Jingang Xiong},
journal= {arXiv preprint arXiv:2407.06757},
year = {2024}
}
Comments
40 pages, comments are welcome