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Stability of a boundary spike layer for the Gierer–Meinhardt system
Title: | Stability of a boundary spike layer for the Gierer–Meinhardt system |
Authors: | Miyamoto, Yasuhito1 Browse this author |
Authors(alt): | 宮本, 安人1 |
Issue Date: | 23-Aug-2005 |
Publisher: | Cambridge University Press |
Journal Title: | European Journal of Applied Mathematics |
Volume: | 16 |
Issue: | 4 |
Start Page: | 467 |
End Page: | 491 |
Publisher DOI: | 10.1017/S0956792505006376 |
Abstract: | We consider the activator-inhibitor Gierer–Meinhardt reaction-diffusion system of biological pattern formation in a closed bounded domain. The existence and stability of a boundary apike-layer solution to the Gierer–Meinhardt model, and it, so-called shadow limit, is analysed. In the limit of small activator diffusivity, together with a large inhibitor diffusivity, an equilibrium boundary spike-layer solution is constructed that concentrates at a non-degenerate critical point $P$ of the boundary. By non-degenerate we mean that every principal curvature of the boundary has a local maximum at $P$, and hence the mean curvature at the boundary has a local maximum at $P$. Rigorous results for the stability of such a boundary spike-layer solution are given. |
Rights: | Copyright © 2005 Cambridge University Press |
Type: | article |
URI: | http://hdl.handle.net/2115/5419 |
Appears in Collections: | 知識メディア・ラボラトリー (Meme Media Laboratory) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 宮本 安人
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