Boundary conditions as symmetry constraints

  • J. D. Crawford
  • M. Golubitsky
  • M. G. M. Gomes
  • E. Knobloch
  • I. N. Stewart
Conference paper

DOI: 10.1007/BFb0085426

Part of the Lecture Notes in Mathematics book series (LNM, volume 1463)
Cite this paper as:
Crawford J.D., Golubitsky M., Gomes M.G.M., Knobloch E., Stewart I.N. (1991) Boundary conditions as symmetry constraints. In: Roberts M., Stewart I. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1463. Springer, Berlin, Heidelberg

Abstract

Fujii, Mimura, and Nishiura [1985] and Armbruster and Dangelmayr [1986, 1987] have observed that reaction-diffusion equations on the interval with Neumann boundary conditions can be viewed as restrictions of similar problems with periodic boundary conditions; and that this extension reveals the presence of additonal symmetry constraints which affect the generic bifurcation phenomena. We show that, more generally, similar observations hold for multi-dimensional rectangular domains with either Neumann or Dirichlet boundary conditions, and analyse the group-theoretic restrictions that this structure imposes upon bifurcations. We discuss a number of examples of these phenomena that arise in applications, including the Taylor-Couette experiment, Rayleigh-Bénard convection, and the Faraday experiment.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • J. D. Crawford
  • M. Golubitsky
  • M. G. M. Gomes
  • E. Knobloch
  • I. N. Stewart

There are no affiliations available

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