オガワ　トシユキ   OGAWA Toshiyuki   小川　知之    所属   明治大学  総合数理学部    職種   専任教授
言語種別	日本語
発行・発表の年月	2005/01
形態種別	学術雑誌
査読	査読あり
標題	Rigorous numerics for localized patterns to the quintic swift-hohenberg equation
執筆形態	共著(筆頭者以外)
掲載誌名	Japan Journal of Industrial and Applied Mathematics
掲載区分	国内
巻・号・頁	22,57-75頁
著者・共著者	Yasuaki Hiraoka, Toshiyuki Ogawa
概要	Localized patterns of the quintic Swift-Hohenberg equation are studied by bifurcation analysis and rigorous numerics. First of all, fundamental bifurcation structures around the trivial solution are investigated by a weak nonlinear analysis based on the center manifold theory. Then bifurcation structures with large amplitude are studied on Galerkin approximated dynamical systems, and a relationship between snaky branch structures of saddle-node bifurcations and localized patterns is discussed. Finally, a topological numerical verification technique proves the existence of several localized patterns as an original infinite dimensional problem, which are beyond the local analysis.
DOI	10.1007/BF03167476
ISSN	09167005
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