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

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Title: Higher dimensional SLEP equation and applications to morphological stability in Polymer Problems
Authors: Nishiura, Yasumasa Browse this author →KAKEN DB
Suzuki, Hiromasa Browse this author
Keywords: singular perturbation
diblock copolymer
reaction diffusion system
pattern formation
matched asymptotic expansion
critical eigenvalues
AMS subject classification = 35B25
AMS subject classification = 35B35
AMS subject classification = 35K57
Issue Date: 2005
Publisher: Society for Industrial and Applied Mathematics
Journal Title: SIAM Journal on Mathematical Analysis
Volume: 36
Issue: 3
Start Page: 916
End Page: 966
Publisher DOI: 10.1137/S0036141002420157
Abstract: 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.
Rights: © 2004 Society for Industrial and Applied Mathematics
Type: article
Appears in Collections:電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 西浦 廉政

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