Spikes for the Two-Dimensional Gierer-Meinhardt System: The Weak Coupling Case

@article{Wei2001SpikesFT,
  title={Spikes for the Two-Dimensional Gierer-Meinhardt System: The Weak Coupling Case},
  author={Juncheng Wei and Matthias Winter},
  journal={Journal of Nonlinear Science},
  year={2001},
  volume={11},
  pages={415-458}
}
Summary. In this paper, we rigorously prove the existence and stability of multiple-peaked patterns that are far from spatial homogeneity for the singularly perturbed Gierer-Meinhardt system in a two-dimensional domain. The Green's function, together with its derivatives, is linked to the peak locations and to the o(1) eigenvalues, which vanish in the limit. On the other hand two nonlocal eigenvalue problems (NLEPs), one of which is new, are related to the O(1) eigenvalues. Under some geometric… CONTINUE READING

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