Abstract

We consider the boundary value problem: which is equivalent to the stationary Keller-Segel system from chemotaxis. Here is a smooth and bounded domain. We show that given any two non-negative integers k, l with k + l ≥ 1, for ε sufficiently small, there exists a solution uε for which develops asymptotically k interior Dirac deltas with weight 8π and l boundary deltas with weight 4π. Location of blow-up points is characterized explicitly in terms of Green's function of the Neumann problem. © 2006 IOP Publishing Ltd and London Mathematical Society.