Keller–Segel model

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.