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

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タイトル: Stability of a boundary spike layer for the Gierer–Meinhardt system
著者: Miyamoto, Yasuhito 著作を一覧する
発行日: 2005年 8月23日
出版者: Cambridge University Press
誌名: European Journal of Applied Mathematics
巻: 16
号: 4
開始ページ: 467
終了ページ: 491
出版社 DOI: 10.1017/S0956792505006376
抄録: 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
資料タイプ: article
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 宮本 安人


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