Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 121, Issue -, Pages 1-46Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.matpur.2018.06.017
Keywords
Pattern formation; Reaction-diffusion system; Spike; Cluster; Stability
Categories
Funding
- NSERC of Canada [NSERC-435557]
Ask authors/readers for more resources
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. (C) 2018 The Authors. Published by Elsevier Masson SAS.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available