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http://bura.brunel.ac.uk/handle/2438/19352| Title: | Stable spike clusters on a compact two-dimensional Riemannian manifold |
| Authors: | Ao, W Wei, J Winter, M |
| Keywords: | pattern formation;mathematical biology;singular perturbation;reaction-diffusion system;Riemannian manifold |
| Issue Date: | 10-Oct-2019 |
| Citation: | Ao, W., Wei, J. and Winter, M. (2020) 'Stable spike clusters on a compact two-dimensional Riemannian manifold', Journal of Differential Equations, 268 (7), pp. 3665 - 3704. doi: 10.1016/j.jde.2019.10.005. |
| Abstract: | Copyright © 2019 The Authors. 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. |
| URI: | https://bura.brunel.ac.uk/handle/2438/19352 |
| DOI: | https://doi.org/10.1016/j.jde.2019.10.005 |
| ISSN: | 0022-0396 |
| Other Identifiers: | ORCID iD: Matthias Winter https://orcid.org/0000-0003-4800-7132 |
| Appears in Collections: | Dept of Mathematics Research Papers |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| FullText.pdf | Copyright © 2019 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (https://creativecommons.org/licenses/by/4.0/). | 1.35 MB | Adobe PDF | View/Open |
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