An introduction to the Keller--Segel equation

par Alejandro Fernández Jiménez (ICJ)

mercredi 22 oct. 2025, 10:00 → 12:00 Europe/Paris

112 (Braconnier)

In the 1970s Patlak, Keller and Segel proposed a system of PDEs in order to study the dynamics of a family  myxamoebas. These myxamoebas experiment a random walk, spreading through space, looking for food, while they are affected by chemotaxis, a natural process which induces the organisms to direct their movement according to certain chemicals concentrated on their surroundings. As a result of combining both behaviours, one obtains a competition between diffusion and aggregation. Since then, there has been an exhaustive effort from the mathematical community in order to understand the properties of this equation and its dichotomy between diffusion and aggregation. In this talk, we will review the existing literature. First, we will focus on the case of dimension two and later we will comment on further cases.