题目：Flow Decomposition and Sharp Integral Fujita Criteria on Weighted Graphs

报告人：孙玉华教授（南开大学数学学院）

时间：2026年9月24日（周四）上午10：30

地点：双清综合楼302教室

摘要：We study the Fujita phenomenon for semilinear heat inequalities generated by variable-speed Laplacians on infinite weighted graphs. Assuming that the graph carries a proper adapted path metric, we establish an integral volume-growth criterion forcing every nonnegative global classical supersolution to vanish, without assuming an initial value.  We prove that a nontrivial supersolution of this kind exists if and only if the equation has a positive global Cauchy solution for some nonzero point-source datum. A complementary heat-kernel construction gives global Cauchy solutions for all sufficiently small point-source data when the same volume integral converges and a matching anchored heat-kernel upper bound is available. 

报告人简介：孙玉华，南开大学数学学院教授，博士生导师。研究方向为黎曼流形及图上的分析，包括椭圆及抛物方程，在包括CPAM，Math. Annalen,JFA,CVPDE,JAM等国际著名期刊发表学术论文30余篇。