A priori bounds of stationary solutions of two dimensional Keller-Segel system on polygonal domains

Abstract

We consider a Neumann boundary problem like Gelfand's problem on polygonal domains and prove that a priori bounds of solutions fail for specific parameters. The same results are already proved by Senba-Suzuki in 2000 when domains are open sets in $\mathbb{R}^2$ with smooth boundaries. The novelty is that the foregoing specific parameters depend on angles of polygonal domains.