Finite time blow-up and chemotactic collapse in Keller-Segel model with signal consumption (Q6566147)

This paper investigates the finite time blow-up phenomenon in the Keller-Segel model. The author uses a backward self-similar solution to demonstrate that finite time blow-up occurs in the model. Specifically, in a one-dimensional space, this blow-up corresponds to the chemotactic collapse phenomenon. In higher-dimensional spaces, the self-similar solution results in blow-up occurring everywhere. The author also examines special cases where the diffusion coefficient of bacteria or oxygen is zero, showing that the chemotactic collapse phenomenon occurs in both one-dimensional and two-dimensional spaces in these scenarios.