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

Toshiyuki Ogawa; Takashi Okuda

doi:10.3934/dcds.2009.25.273

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2009, Volume 25, Issue 1: 273-297. Doi: 10.3934/dcds.2009.25.273

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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

Received: September 30, 2007

Revised: May 31, 2008

Published: December 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K57, 37L10; Secondary: 35B32.

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