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Existence of Spikes for the Gierer-Meinhardt System in One Dimension

  • Juncheng Wei
  • Matthias Winter
Part of the Applied Mathematical Sciences book series (AMS, volume 189)

Abstract

We give a full account of the existence of multiple spikes for the Gierer-Meinhardt system in an interval on the real line. We present a unified rigorous approach based on the Liapunov-Schmidt method which is very flexible and consider the cases of symmetric and asymmetric multi-spike solutions. We also study clustered multiple spikes.

Keywords

Implicit Function Theorem Multiple Cluster Geometric Singular Perturbation Theory Multiple Spike Order Normal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Juncheng Wei
    • 1
  • Matthias Winter
    • 2
  1. 1.Department of MathematicsThe Chinese University of Hong KongHong KongChina
  2. 2.Department of Mathematical SciencesBrunel UniversityUxbridgeUK

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