Geometric PDE and Applied Analysis Seminar (September 7, 2023)

Title: Behavior of solutions to systems related to Keller-Segel system

Speaker: Prof. Takasi Senba (Fukuoka University)

Abstract: It is known that two dimensional Keller-Segel system has a critical number on \(L^1\)-norm of solutions. That is to say, solutions to the Keller-Segel system exist globally in time, if those \(L^1\)-norm are less than the critical number. And, there are blow-up solutions whose \(L^1\)-norm are bigger than the critical number. Some systems related to Keller-Segel system are expected to have critical numbers for any dimensional cases. In this talk, we will introduce conjectures on those critical numbers and some evidences for those conjectures.