Work

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

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2407.06757

Authors: Jin, Tianling, Xiong, Jingang

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G2210630433, G6591056831, G7726240407

OpenAlex ID: W4400518946

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