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DC Field | Value | Language |
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dc.contributor.author | Ao, W | - |
dc.contributor.author | Wei, J | - |
dc.contributor.author | Winter, M | - |
dc.date.accessioned | 2017-08-07T09:28:52Z | - |
dc.date.available | 2017-08-07T09:28:52Z | - |
dc.date.issued | 2018-06-28 | - |
dc.identifier.citation | Ao, W., Wei, J. and Winter, M. (2019) 'Stable boundary spike clusters for the two-dimensional Gierer-Meinhardt system', Journal de Mathématiques Pures et Appliquées, 121, pp. 1-46. doi: 10.1016/j.matpur.2018.06.017. | en_US |
dc.identifier.issn | 0021-7824 | - |
dc.identifier.uri | https://bura.brunel.ac.uk/handle/2438/14992 | - |
dc.description.abstract | © 2018 The Authors. 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. | en_US |
dc.description.sponsorship | NSERC of Canada (grant number NSERC-435557). | - |
dc.format.extent | 1 - 46 | - |
dc.format.medium | Print-Electronic | - |
dc.language.iso | en | en_US |
dc.rights | © 2018 The Authors. Published by Elsevier Masson SAS. This is an open access article under the CC BY license (https://creativecommons.org/licenses/by/4.0/). | - |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | - |
dc.subject | pattern formation | en_US |
dc.subject | reaction-diffusion system | en_US |
dc.subject | spike | en_US |
dc.subject | cluster | en_US |
dc.subject | stability | en_US |
dc.title | Stable boundary spike clusters for the two-dimensional Gierer-Meinhardt system | en_US |
dc.type | Article | en_US |
dc.identifier.doi | https://doi.org/10.1016/j.matpur.2018.06.017 | - |
dc.relation.isPartOf | Journal de Mathématiques Pures et Appliquées | - |
pubs.publication-status | Published | - |
pubs.volume | 121 | - |
dc.identifier.eissn | 1776-3371 | - |
Appears in Collections: | Dept of Mathematics Research Papers |
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