Boundary Spikes in the Gierer-Meinhardt System




Manuel del Pino
Departamento de Ingenería Matemática F.C.F.M.
Universidad de Chile
Casilla 170 Correro 3, Santiago, CHILE



Patricio Felmer
Departamento de Ingenería Matemática F.C.F.M.
Universidad de Chile
Casilla 170 Correro 3, Santiago, CHILE



Michal Kowalczyk
Carnegie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA 15213




ABSTRACT:

In this paper we consider the Gierer-Meinhardt system which models biochemical reactions of the activator-inhibitor type. Assuming that the rate of diffusion of the activator is small, while the rate of diffusion of the inhibitor is large we show the existence of steady-state solutions concentrating at (topologically nontrivial) critical points of the mean curvature of the domain.

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