Higher dimensional SLEP equation and applications to morphological stability in Polymer Problems

Nishiura, Yasumasa; Suzuki, Hiromasa

Higher dimensional SLEP equation and applications to morphological stability in Polymer Problems

Nishiura, Yasumasa; Suzuki, Hiromasa

SIAM Journal on Mathematical Analysis, 2005, 36(3), 916-966

Permalink : https://hdl.handle.net/2115/35224

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アクセス権	open access
URI	https://hdl.handle.net/2115/35224
タイトル	Higher dimensional SLEP equation and applications to morphological stability in Polymer Problems
著者	e-Rad_Researcher 00131277 著者名 Nishiura, Yasumasa
著者	著者名 Suzuki, Hiromasa
言語	英語
キーワード	singular perturbation
	diblock copolymer
	reaction diffusion system
	pattern formation
	matched asymptotic expansion
	stability
	critical eigenvalues
	AMS subject classification = 35B25
	AMS subject classification = 35B35
	AMS subject classification = 35K57
発行日	2005
出版者	Society for Industrial and Applied Mathematics
収録物名	SIAM Journal on Mathematical Analysis
巻(号)	36(3)
ページ	916-966
抄録	Existence and stability of stationary internal layered solutions to a rescaled diblock copolymer equation are studied in higher dimensional space. Rescaling is necessary since the characteristic domain size of any stable pattern eventually vanishes in an appropriate singular limit. A general sufficient condition for the existence of singularly perturbed solutions and the associated stability criterion are given in the form of linear operators acting only on the limiting location of the interface. Applying the results to radially symmetric and planar patterns, we can show, for instance, stability of radially symmetric patterns when one of the components of diblock copolymer dominates the other, and that of the long-striped pattern in a long and narrow domain for the planar case. These results are consistent with the experimental ones. The above existence and stability criterion can be easily extended to a class of reaction diffusion systems of activator-inhibitor type.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
権利情報	© 2004 Society for Industrial and Applied Mathematics
PISSN	0036-1410
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1137/S0036141002420157