Blow‐Up in the Critical Quasilinear Keller–Segel System With Indirect Signal Production
Abstract
ABSTRACT We study the Neumann initial‐boundary value problem for the following quasilinear chemotaxis system with indirect signal production in with . Here , for all . We prove that and decide about the occurrence of blow‐up: namely, it is seen that if then at each appropriately large mass level , there exist radial initial data such that , and that the associated solution blows up either in finite or in infinite time. Especially, if or then the blow‐up can only happen in infinite time.
Fields of Study & Subjects
Mathematical Biology Tumor Growth
Nonlinear Partial Differential Equations
Nonlinear Dynamics and Pattern Formation
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Volume
- 49
- Issue
- 10
- Pages
- 10149–10172
- Publication date
- 13 February 2026
- Language
- EN