Patterns in the Keller–Segel system with density cut-off
Abstract
The Patlak–Keller–Segel system with logistic sensitivity has been widely advocated as a model which avoids overcrowding and generates complex patterns. Here we also consider the general case of a nonlinear diffusion of porous medium type with exponent $m$. The complexity of the observed patterns makes it complicated to understand the processes at work. Here, we analyze the pattern formation ability of such a system, which depends highly on $m$ and three different analyzes are needed for $m=1$ (linear diffusion), for $1\ 2$ but not for $m 1}$.
Fields of Study & Subjects
Mathematical Biology Tumor Growth
advanced mathematical theories
Gene Regulatory Network Analysis
Publication details
- Journal / source
- EMS series of congress reports
- Pages
- 219–255
- Publication date
- 20 June 2026
- Language
- EN
- Document type
- Book chapter