Boundary concentration phenomena for the higher-dimensional Keller-Segel system

Abstract

We study the existence of steady states to the Keller-Segel system with linear chemotactical sensitivity function on a smooth bounded domain in ${\mathbb{R}}^N,$ $N\ge 3,$ having rotational symmetry. We find three different types of chemoattractant concentration which concentrate along suitable $(N-2)-$dimensional minimal submanifolds of the boundary. The corresponding density of the cellular slime molds exhibit in the limit one or more Dirac measures supported on those boundary submanifolds.