Boundary spikes in the Gierer-Meinhardt system
Manuel del Pino, Patricio L. Felmer, Michał Kowalczyk · Communications on Pure & Applied Analysis · 2002
In this paper we consider the Gierer-Meinhardt system in dimension $N=2,3$. Assuming small diffusion of the activator $\varepsilon$ « 1 and large diffusion of the inhibitor $D$ » $1/\varepsilon^N$ we show that there exists a solution to the Gierer-Meinhardt system such that the activator is concentrated at the critical point of the curvature of the domain. To establish this result we use the topological degree argument.