Stability vs. instability of singular steady states in the parabolic-elliptic Keller-Segel system on ${\mathbb{R}}^n$

Francesca Colasuonno, Michael Winkler

The Cauchy problem in ${\mathbb{R}}^n$ is considered for \begin{eqnarray*} \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot (u\nabla v),\\ 0 = Δv + u. \end{array} \right. \end{eqnarra…