Stable spike clusters on a compact two-dimensional Riemannian manifold

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Ao, Weiwei¹  Wei, Juncheng²  Winter, Matthias³ 

[1] Wuhan Univ, Dept Math, Wuhan 430072, Peoples R China

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[3] Brunel Univ London, Dept Math, Uxbridge UB8 3PH, Middx, England

关键词: Pattern formation;    Mathematical biology;    Singular perturbation;    Reaction-diffusion system;    Riemannian manifold;   

DOI  :  10.1016/j.jde.2019.10.005

来源: Elsevier

【 摘 要 】

We consider the Gierer-Meinhardt system with small inhibitor diffusivity and very small activator diffusivity on a compact two-dimensional Riemannian manifold without boundary. We study steady state solutions which are far from spatial homogeneity. We construct two different spike clusters, each consisting of two spikes, which both approach the same nondegenerate local maximum point of the Gaussian curvature. We show that one of these spike clusters is stable, the other one is unstable. (C) 2019 The Authors. Published by Elsevier Inc.

【 授权许可】

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