Nonexistence of Higher Dimensional Stable Turing Patterns in the Singular Limit

Nishiura, Yasumasa; Suzuki, Hiromasa

SIAM Journal on Mathematical Analysis, 1998, 29(5), 1087-1105

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アクセス権
open access
URI
https://hdl.handle.net/2115/39999
タイトル
Nonexistence of Higher Dimensional Stable Turing Patterns in the Singular Limit
著者
e-Rad_Researcher
00131277
著者名
Nishiura, Yasumasa
著者名
Suzuki, Hiromasa
言語
英語
キーワード
reaction-diffusion system
interfacial pattern
singular perturbation
matched asymptotic expansion
MSC=35B25
MSC=35B35
MSC=35K57
MSC=35R35
発行日
1998-09
出版者
Society for Industrial and Applied Mathematics
収録物名
SIAM Journal on Mathematical Analysis
巻(号)
29(5)
ページ
1087-1105
抄録
When the thickness of the interface (denoted by ε) tends to zero, any stable stationary internal layered solutions to a class of reaction-diffusion systems cannot have a smooth limiting interfacial configuration. This means that if the limiting configuration of the interface has a smooth limit, it must become unstable for smallε, which makes a sharp contrast with the one-dimensional case. This suggests that stable layered patterns must become very fine and complicated in this singular limit. In fact we can formally derive that the rate of shrinking of stable patterns is of orderε^[1/3]. Using this scaling, the resulting rescaled reduced equation determines the morphology of magnified patterns. A variational characterization of the critical eigenvalue combined with the matched asymptotic expansion method is a key ingredient for the proof, although the original linearized system is not of self-adjoint type.
資源タイプ
学術雑誌論文
出版タイプ
Version of Record
権利情報
Copyright © 1998 Society for Industrial and Applied Mathematics
PISSN
0036-1410
EISSN
1095-7154
NCID
AA00424217
関連情報 (isIdenticalTo)
出版社版DOI
https://doi.org/10.1137/S0036141096313239