Special Session 82: Recent Advances in Nonlinear PDEs and Free Boundary Problems

One bubble dynamics for the Sobolev critical fast diffusion equation in bounded domains

Tianling Jin
The Hong Kong University of Science and Technology
Hong Kong
Co-Author(s):    Jingang Xiong
Abstract:
We will discuss 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 will show the dichotomy that every solution converges uniformly, in terms of relative error, to either a steady state or a blowing-up bubble.