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.
Citation
Yoshifumi Mimura. "A priori bounds of stationary solutions of two dimensional Keller-Segel system on polygonal domains." Differential Integral Equations 28 (3/4) 347 - 360, March/April 2015. https://doi.org/10.57262/die/1423055232
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