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June  2006, 5(2): 383-393. doi: 10.3934/cpaa.2006.5.383

Bifurcation analysis to Rayleigh-Bénard convection in finite box with up-down symmetry

Toshiyuki Ogawa 1,

1. 

Graduate School of Engineering Science, Osaka University, 560-8531 Toyonaka, Japan

Received  February 2005 Revised  June 2005 Published  March 2006

Rayleigh-Bénard convection in a small rectangular domain is studied by the standard bifurcation analysis. The dynamics on the center manifold is calculated up to 3rd order. By this normal form, it is possible to determine the local bifurcation structures in principle. One can easily imagine that mixed mode solutions such as hexagonal, patchwork-quilt patterns are unstable from the knowledge of amplitude equation:Ginzburg-Landau equation. However they are not necessarily similar to each other in a small rectangular domain. Several non-trivial stable mixed mode patterns are introduced.
Keywords: bifurcation analysis, normal form., Rayleigh-Bénard convection.
Mathematics Subject Classification: 35B32, 37G05 ,76E0.
Citation: Toshiyuki Ogawa. Bifurcation analysis to Rayleigh-Bénard convection in finite box with up-down symmetry. Communications on Pure & Applied Analysis, 2006, 5 (2) : 383-393. doi: 10.3934/cpaa.2006.5.383
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