Large mass boundary condensation patterns in the stationary Keller-Segel system (Q2630911)

The authors are concerned with the study of \(-\Delta u+u=\lambda e^u\) in \(\Omega\), subject to homogeneous Neumann boundary condition. Here \(\Omega\subset \mathbb R^2\) is a smooth and bounded domain and \(\lambda>0\) is a parameter. As it is explained in the paper, the above problem is equivalent to the stationary Keller-Segel system via the change \(v=\lambda e^u\). The authors establish the existence of large mass solutions \(u_\lambda\) which exhibit a sharp boundary layer along the entire boundary of the domain as \(\lambda\) tends to zero.