---
tag: K04XRMH820
kind: concept
name: Keller–Segel model
msc: [35Q92, 92C17, 35K57]
sources:
  - url: https://en.wikipedia.org/wiki/Chemotaxis
---

## Summary

The Keller–Segel model is a system of parabolic equations for chemotaxis, the motion of cells toward a chemical signal that they produce themselves.
It was proposed by Keller and Segel in 1970 to describe the aggregation of slime mould amoebae.
The cells diffuse and drift up the gradient of the chemical, and this self-attraction can make the cell density concentrate.
In two dimensions the total mass decides between global existence and blow-up in finite time.
This makes the model a standard test case for blow-up in parabolic systems.

## Explanations

### L1 human

Imagine cells that release a scent and also like to move toward where the scent is strong.
Random motion spreads the cells out, while the scent pulls them together.
If there are few cells, spreading wins and the cells stay spread out.
If there are many, attraction wins and the cells collapse into a dense cluster.