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2002, Volume 1, Issue 4: 437-456. Doi: 10.3934/cpaa.2002.1.437
This issue Previous Article Next Article Some existence and concentration results for nonlinear Schrödinger equations

Boundary spikes in the Gierer-Meinhardt system

  • 1.

    Departamento de Ingeneria Matematica F.C.F.M., Casilla 170 Correro 3, Santiago

  • 2.

    Departamento de Ingeneria Matematica F.C.F.M., Universidad de Chile, Casilla 170 Correro 3, Santiago

  • 3.

    Department of Mathematical Sciences, Kent State University, Kent, OH 44242

Received:  January 2002
Revised:  July 2002
Published:  December 2002
Abstract / Introduction Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: 35J25, 35B25.

    Citation:
    shu

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