中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: Jingang Xiong (Beijing Normal University)
Inviter: 阮国兴
Language: English
Title: Optimal Weighted Smoothing and Classification of Ancient Solutions for Fast Diffusion Equations
Time & Venue: 2026年3月10日（星期二）14：00-15：00 & S803
Abstract: We study the zero-Dirichlet problem for the fast diffusion equation on smooth bounded domains. We establish a sharp weighted smoothing estimate and show that the Brezis–Turner exponent is critical in this context. As an application, we obtain a complete classification of ancient solutions in the subcritical regime (i.e., below the Brezis–Turner exponent). In the supercritical case (above this exponent), we provide evidence suggesting the existence of nontrivial self-similar ancient solutions, which we will discuss in detail. This is joint work with Xiqin Jiang and Huayang Wang.