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February  2009, 25(1): 273-297. doi: 10.3934/dcds.2009.25.273

Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions

Toshiyuki Ogawa 1, and  Takashi Okuda 2,

1. 

Graduate School of Engineering Science, Osaka University, 560-8531 Toyonaka
2. 

Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337, Japan

Received  October 2007 Revised  June 2008 Published  June 2009

Bifurcation structure of the stationary solutions to the Swift-Hohenberg equation with a symmetry breaking boundary condition is studied. Namely, a SO(2) breaking perturbation is added to the Neumann or Dirichlet boundary conditions. As a result, half of the secondary bifurcation points change their characters by the imperfection of pitchfork bifurcations.
Keywords: avoid-crossing., imperfect bifurcation, Swift-Hohenberg equation, symmetry breaking boundary condition, activator-inhibitor system.
Mathematics Subject Classification: Primary: 35K57, 37L10; Secondary: 35B3.
Citation: Toshiyuki Ogawa, Takashi Okuda. Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions. Discrete & Continuous Dynamical Systems, 2009, 25 (1) : 273-297. doi: 10.3934/dcds.2009.25.273
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