Special Session 58: 

Radial solutions to the Keller-Segel equation

Jean-Baptiste Casteras
Universite Libre de Bruxelles
Belgium
Co-Author(s):    
Abstract:
In this talk, we will be interested in the Keller-Segel equation $$\begin{cases}-\Delta u+u=\lambda e^u ,\ u>0, \text{ in } \Omega,\ \partial u=0, \text{ on } \partial \Omega, \end{cases}$$ where $\Omega \subset \R^N$, $N\geq 2$ and $\lambda>0$. This equation arises when looking for steady states to the Keller-Segel system which describes chemiotaxis phenomena. We will make a radial bifurcation analysis of this equation with respect to the parameter $\lambda$ and describe the solutions when $\lambda \rightarrow 0^+$. Joint works with Denis Bonheure, Juraj F\ oldes, Benedetta Noris and Carlos Rom\` an.