# American Institute of Mathematical Sciences

December  2002, 1(4): 437-456. doi: 10.3934/cpaa.2002.1.437

## Boundary spikes in the Gierer-Meinhardt system

 1 Departamento de Ingeneria Matematica F.C.F.M., Casilla 170 Correro 3, Santiago, Chile 2 Departamento de Ingeneria Matematica F.C.F.M., Universidad de Chile, Casilla 170 Correro 3, Santiago, Chile 3 Department of Mathematical Sciences, Kent State University, Kent, OH 44242, United States

Received  January 2002 Revised  July 2002 Published  September 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.
Citation: Manuel del Pino, Patricio Felmer, Michal Kowalczyk. Boundary spikes in the Gierer-Meinhardt system. Communications on Pure & Applied Analysis, 2002, 1 (4) : 437-456. doi: 10.3934/cpaa.2002.1.437
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