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Title: Stable boundary spike clusters for the two-dimensional Gierer-Meinhardt system
Authors: Winter, M
Wei, J
Ao, W
Keywords: Pattern formation;Reaction-diffusion system;Spike;Cluster;Stability
Issue Date: 2017
Citation: Journal de Mathématiques Pures et Appliquées
Abstract: We consider the Gierer-Meinhardt system with small inhibitor diffusivity and very small activator diffusivity in a bounded and smooth two-dimensional domain. For any given positive integer k we construct a spike cluster consisting of k boundary spikes which all approach the same nondegenerate local maximum point of the boundary curvature. We show that this spike cluster is linearly stable. The main idea underpinning these stable spike clusters is the following: due to the small inhibitor diffusivity the interaction between spikes is repulsive and the spikes are attracted towards a nondegenerate local maximum point of the boundary curvature. Combining these two effects can lead to an equilibrium of spike positions within the cluster such that the cluster is linearly stable.
ISSN: 0021-7824
Appears in Collections:Dept of Mathematics Embargoed Research Papers

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