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

Boundary spikes in the Gierer-Meinhardt system

Manuel del Pino 1, , Patricio Felmer 2, and  Michal Kowalczyk 3,

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.
Keywords: Gierer-Meinhardt system, spikes, topological degree..
Mathematics Subject Classification: 35J25, 35B2.
Citation: Manuel del Pino, Patricio Felmer, Michal Kowalczyk. Boundary spikes in the Gierer-Meinhardt system. Communications on Pure and Applied Analysis, 2002, 1 (4) : 437-456. doi: 10.3934/cpaa.2002.1.437
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