2022/10/21 by Chen, Hua, Li, Jian-Meng, Wang, Kelei
#35B33 #35B44 #35K58 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2210.12299
In this paper we develop a blow up theory for the parabolic-elliptic Keller-Segel system, which can be viewed as a parabolic counterpart to the Liouville equation. This theory is applied to the study of first time singularities, ancient solutions and entire solutions, leading to a description of the blow-up limit in the first problem, and the large scale structure in the other two problems.