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Title: Bifurcations for Turing instability without SO(2) symmetry (English)
Author: Ogawa, Toshiyuki
Author: Okuda, Takashi
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 43
Issue: 6
Year: 2007
Pages: 869-877
Summary lang: English
Category: math
Summary: In this paper, we consider the Swift–Hohenberg equation with perturbed boundary conditions. We do not a priori know the eigenfunctions for the linearized problem since the ${\rm SO(2)}$ symmetry of the problem is broken by perturbation. We show that how the neutral stability curves change and, as a result, how the bifurcation diagrams change by the perturbation of the boundary conditions. (English)
Keyword: perturbed boundary conditions
Keyword: imperfect pitchfork bifurcation
Keyword: Turing instability
MSC: 35B32
MSC: 35K20
MSC: 35K55
MSC: 37G40
MSC: 37L10
MSC: 37L20
idZBL: Zbl 1136.37042
idMR: MR2388400
Date available: 2009-09-24T20:30:36Z
Last updated: 2013-09-21
Stable URL:
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Reference: [7] Ogawa T., Okuda T.: Bifurcation analysis to Swift–Hohenberg equation with perturbed boundary conditions.In preparation Zbl 1221.37157
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