Work

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison

Year: 2025

Type: article

Abstract: We study the Neumann initial-boundary value problem for the parabolic-elliptic chemotaxis system, proposed by Jäger and Luckhaus (1992). We confirm that their comparison methods can be simplified and refined, applicable to seek the critical mass 8π concerning finite-time blow-up in the unit disk. As an application, we deal with a parabolic–elliptic–parabolic chemotaxis model involving indirect signal production in the unit ball of R 4 , proposed by Tao and Winkler (2025). Within the framework of radially symmetric solutions, we prove that if initial mass is less than 64 π 2 , then solution is globally bounded; for any m exceeding 64 π 2 , there exist non-negative initial data with prescribed mass m such that the corresponding classical solutions exhibit a formation of Dirac-delta type singularity in finite time, termed a chemotactic collapse.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ae05a9

Authors: Xuan Mao, Meng Liu, Yuxiang Li

Institutions: Hohai University, Anhui University of Technology, Southeast University

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G3291893717, 非线性Keller-Segel方程的定性研究, G4021010997