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Stability of a boundary spike layer for the Gierer–Meinhardt system

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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)

Submitter: 宮本 安人

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