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An instability criterion for activator–inhibitor systems in a two-dimensional ball

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タイトル: An instability criterion for activator–inhibitor systems in a two-dimensional ball
著者: Miyamoto, Yasuhito 著作を一覧する
キーワード: Instability
Activator–inhibitor system
Shadow system
Reaction–diffusion system
Nodal curve
Nodal domain
発行日: 2006年10月15日
出版者: Elsevier Inc.
誌名: Journal of Differential Equations
巻: 229
号: 2
開始ページ: 494
終了ページ: 508
出版社 DOI: 10.1016/j.jde.2006.03.015
抄録: Let B be a two-dimensional ball with radius R. Let(u(x,y),ξ) be a non-constant steady state of the shadow system ut=Du∆u+f(u,ξ) in B×R+ and τξt =1/|B|∬Bg(u,ξ)dxdy in R+, ∂νu=0 on∂B×R+, where f and g satisfy the following:fξ(u,ξ)<0,gξ(u,ξ) <0 and there is a function k(ξ) such that gu(u,ξ)=k(ξ)fξ(u,ξ). This system includes a special case of the Gierer-Meinhardt system and the FitzHugh-Nagumo system. We show that if Z [Uθ(・)] ≥3, then(u,ξ)is unstable for all τ>0, where U(θ):=u(Rcosθ,Rsinθ) and Z [w(・)] denotes the cardinal number of the zero level set of w(・)∈Cº(R/2πZ). The contrapositive of this result is the following: if(u,ξ)is stable for someτ>0, then Z[Uθ(・)]=2. In the proof of these results, we use a strong continuation property of partial differential operators of second order on the boundary of the domain.
Relation (URI):
資料タイプ: article (author version)
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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